> **Source:** https://permissionless.fi/en/23-volatility-clustering
> From *Permissionless Finance* (Permissionless Finance: From Perpetual Futures to the On-Chain Global Market) by Eric Cheung. Licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/).

# Chapter 23: The Microstructural Mechanisms of Volatility Clustering

The volatility of Bitcoin perpetual futures follows a pattern no statistician can ignore: high volatility tends to follow high volatility, and low volatility tends to follow low volatility. In cryptocurrency markets, this volatility clustering is more pronounced and more persistent than in traditional financial assets. Empirical research shows that the probability of volatility clustering in crypto assets—high volatility persistently followed by high volatility—is significantly higher than in traditional financial assets [1]. This characteristic implies that volatility is not pure white noise but possesses deep long-memory properties. Generalized autoregressive conditional heteroskedasticity (GARCH) models and their variants (detailed in Section 23.1.1) can capture this clustering at the statistical level [2]. However, the successful fit of a statistical model is merely a mathematical description of the phenomenon; it does not answer a more fundamental economic question: why does the current conditional variance depend on past shocks? What exactly is the microstructural mechanism that drives this volatility memory and clustering?

This question marks the starting point for a deeper investigation into volatility dynamics. Statistical description tells us that high volatility is more likely to follow high volatility, but understanding and predicting market behavior requires uncovering the causal chain behind the data. In perpetual futures markets, volatility is not determined independently by a single random event; rather, it is shaped jointly by a series of interwoven market frictions, institutional designs, and participant behaviors. When an exogenous information shock breaks the market's calm, it alters not only the current price but also the market's liquidity depth, the level of systemic leverage, and market makers' risk appetite. Changes in these variables set new initial conditions for the next period's price movement, so that a new shock of the same magnitude can produce a volatility response far exceeding the norm under the new market state. The microstructural mechanism of volatility clustering therefore lies in how the market state, evolving on its own across different time scales, amplifies external shocks.

To explain this process systematically, this chapter constructs a three-layer explanatory framework composed of slow variables, feedback loops, and a state machine. At the lowest layer, the macroeconomic environment, the level of systemic leverage, and liquidity depth act as slow variables that evolve gradually over longer time scales, setting the baseline for market fragility. These slow variables do not directly generate violent price swings, but they determine the system's capacity to absorb external shocks. At the intermediate layer, strong positive feedback loops form between volatility and liquidity, between volatility and leverage, and between volatility and participant behavior. Once the slow variables accumulate to a critical point, a minor triggering event can activate these feedback loops, causing shocks to be continuously amplified rather than dampened within the system. At the top layer, the interaction of these mechanisms manifests as nonlinear jumps of the market among three discrete states: calm, stressed, and crisis. These three layers of mechanism may exist in any leveraged market, but the institutional design specific to perpetual futures—the buffer-free transmission of liquidation cascades, the pulse-superposition effect of funding rates, and the around-the-clock trading environment with no market close—imposes systematic amplification on all three layers, explaining why the volatility clustering effect in crypto markets far exceeds that of traditional assets. This chapter also reveals that the accumulation rate of systemic risk often peaks during low-volatility periods, and it ties all the theoretical components together through a complete volatility life-cycle case study.

Dissecting these three layers of mechanism one by one moves the analysis beyond a purely statistical view of volatility toward one grounded in market microstructure and dynamics. Grasping how slow variables gradually accumulate fragility, how feedback loops amplify shocks, and how the state machine drives regime transitions not only explains why high-volatility events cluster in the time series; it also provides a solid theoretical foundation and a structured framework for building forward-looking volatility forecasting models and dynamic risk management strategies in the next chapter.

## 23.1 The empirical facts of volatility clustering

Financial asset time series commonly exhibit a statistical feature known as *volatility clustering*: large price movements tend to be followed by large price movements, while small price movements tend to be followed by small price movements. In crypto assets, and especially in perpetual futures markets, this clustering effect is particularly severe. Using empirical data and econometric models, this section establishes the empirical facts of volatility clustering in perpetual futures markets and compares them quantitatively with traditional financial markets. It aims not only to describe the phenomenon precisely but also to motivate the inquiry into the underlying microstructural mechanisms that follows.

### 23.1.1 Definition and measurement

The essence of volatility clustering is the persistence over time of the variance of asset returns. Operationally, this persistence is most often measured through the GARCH model. Since Engle (1982) introduced the autoregressive conditional heteroskedasticity (ARCH) model and Bollerslev (1986) generalized it into the GARCH form, this framework has become the standard tool for characterizing volatility clustering in financial time series [3][4]. The model assumes that the current conditional variance depends not only on past squared returns (i.e., external shocks) but also on past conditional variances. The standard form of the GARCH(1,1) variance equation is:

$$\sigma_t^2 = \omega + \alpha \epsilon_{t-1}^2 + \beta \sigma_{t-1}^2$$

where $\sigma_t^2$ is the conditional variance in period $t$, $\omega > 0$ is a constant term (which determines the long-run variance level), $\epsilon_{t-1}$ is the return residual from the previous period (i.e., the external shock), $\alpha \geq 0$ measures the immediate impact of new information shocks on volatility, and $\beta \geq 0$ measures the memory effect of historical volatility on current volatility. Their sum, $\alpha + \beta$, is called the volatility persistence parameter; the closer its value is to 1, the stronger the volatility clustering effect—that is, the longer high-volatility or low-volatility states persist [5] (when $\alpha + \beta < 1$, the process is covariance-stationary, and the half-life of a shock is $\ln 0.5 / \ln(\alpha + \beta)$).

In most traditional financial assets, this persistence parameter typically falls within the range of 0.95 to 0.99. This means that a major market shock triggers not only violent volatility on the day itself but also an effect that persists, in diminishing fashion, over the following weeks or even months. This slowly decaying process constitutes the volatility half-life—the time required for a shock's impact to halve. For assets with a high persistence parameter, the volatility half-life can extend to several weeks. Beyond parameter estimation, volatility clustering can also be observed directly through the autocorrelation function of realized volatility. In an idealized random-walk market that lacks any clustering effect, the autocorrelation coefficients of realized volatility should decay rapidly to zero; in real markets, however, these coefficients often remain significantly positive across many lag orders, confirming the self-perpetuating character of volatility states.

Figure 23-1 uses a GARCH(1,1) model to simulate the conditional volatility of BTC perpetual futures across a typical market cycle.

![Figure 23-1](./images/fig-23-1-en.png)

**Figure 23-1.** The clustering pattern of BTC perpetual futures volatility (Simulated by the author using a GARCH(1,1) model; parameters: ω=0.00001, α=0.08, β=0.90, sample length 2,000 days; illustrative simulation, not empirical data)

In Figure 23-1, volatility is not uniformly distributed but exhibits a clearly clustered structure: each high-volatility cluster contains multiple consecutive days of extreme movement. When the market moves from a calm period into a stressed or crisis period, the volatility baseline rises markedly and sustains itself for a considerable time, until the intrinsic constraints of market mechanisms gradually exhaust it. This clustered distribution is precisely the intuitive manifestation of $\alpha + \beta$ approaching 1 in the GARCH model: past shocks, through the path dependence of the conditional variance, continuously transmit energy along the time series.

### 23.1.2 Cross-market quantitative comparison

Comparing crypto-asset perpetual futures with traditional financial markets more clearly delineates the distinctiveness of their volatility clustering. Empirical research shows that the returns of major crypto assets such as BTC and ETH not only exhibit the leptokurtic, fat-tailed features similar to those of traditional markets, but that the intensity of their volatility clustering is significantly higher than that of traditional assets across multiple dimensions [6]. This difference does not stem simply from the innate "high volatility" of crypto assets; rather, it is deeply rooted in their specific market microstructure and derivatives design.

To quantify the specific magnitude of this difference, Table 23-1 systematically compares BTC perpetual futures, BTC spot, and S&P 500 index futures across five dimensions: the persistence parameter, the autocorrelation coefficient, the half-life, the duration of clustering episodes, and average volatility.

| Metric | BTC perpetual futures | CME BTC futures | BTC spot | S&P 500 futures |
| :--- | :--- | :--- | :--- | :--- |
| GARCH(1,1) α+β | 0.97–0.99 | 0.95–0.97 | 0.95–0.98 | 0.95–0.98 |
| Daily autocorrelation of realized volatility | 0.65–0.80 | 0.60–0.74 | 0.58–0.72 | 0.55–0.70 |
| Volatility half-life (days) | 15–40 | 12–28 | 12–30 | 10–25 |
| Duration of extreme volatility clusters (days) | 5–15 | 4–10 | 4–10 | 3–8 |
| Average daily volatility (%) | 3.5–5.2 | 3.3–4.9 | 3.2–4.8 | 1.2–1.8 |

**Table 23-1.** Cross-market quantitative comparison of volatility clustering intensity (Data source: the author's directional estimates synthesized from multiple sources; the specific ranges are not reported cell-by-cell from a single source [6][1])

The quantitative comparison reveals several key facts. The most diagnostically valuable contrast in the table is not the difference between BTC perpetual futures and the S&P 500 (the two differ fundamentally in the risk premium and volatility level of the underlying asset), but the difference between BTC perpetual futures and CME BTC futures, because the two share the same underlying asset yet differ significantly in institutional design (CME uses a traditional margin-call mechanism, imposes trading-session limits, and sets lower leverage caps). BTC perpetual futures are systematically higher than CME BTC futures in both the persistence parameter and the half-life, a difference that points more cleanly to the institutional amplification effect of perpetual futures than to the volatility characteristics of the underlying asset itself. The α+β ranges of BTC perpetual futures and BTC spot do overlap (0.97–0.99 versus 0.95–0.98), so this difference may not be statistically significant, and the magnitude of the institutional amplification effect requires rigorous testing on larger samples. The high persistence of BTC perpetual futures may also be driven partly by macro factors, such as the volatility cycles of the VIX and the U.S. dollar index, rather than being entirely endogenous to the perpetual futures mechanism, and this motivates the slow-variable analysis in Section 23.2. The duration of extreme volatility clusters in perpetual futures is significantly longer than in traditional markets or CME BTC futures, and this prolonged high-pressure state places extremely high demands on market makers' inventory management and risk control.

### 23.1.3 Nonlinear clustering features

Traditional autoregressive models tend to depict volatility clustering as a smooth, symmetric, slowly decaying process. In perpetual futures markets, however, the clustering phenomenon exhibits more complex nonlinear features. Cont (2007) [7], using an agent-based simulation model, showed that when trend followers and fundamental traders interact dynamically in the market, volatility clustering can arise spontaneously as an emergent property, without any exogenous GARCH structure. The analysis in this chapter is complementary to Cont's agent-based model: Cont's model focuses on how information diffusion and strategy imitation generate clustering in the cross-section, whereas this chapter's three-layer framework focuses on how leverage, liquidity, and liquidation mechanisms sustain and amplify clustering along the time series. Together they point to the multi-source origins of volatility clustering. These nonlinear features challenge simple statistical descriptions and call for a more refined mechanistic analysis.

Tail clustering is a prominent nonlinear feature of crypto-asset markets. Extreme volatility events—that is, observations in the tails of the return distribution—rarely occur in isolation; instead, they tend to erupt in bursts within a short period. This phenomenon is already evident in the distribution of extreme funding-rate values, and along the volatility dimension it manifests as a single 5-standard-deviation shock often rapidly inducing several subsequent shocks of 3 to 4 standard deviations [8]. Such bursts of extreme events indicate that the market's risk-absorption capacity is structurally damaged after the first shock, so that subsequent minor disturbances can also trigger violent price responses.

Jump clustering describes the discontinuous transition of volatility states. In perpetual futures, the rise in volatility is often not gradual but accompanied by jump-like discontinuities in price. After the market experiences a liquidation cascade triggered by leverage unwinding, the probability of a second or even third cascade occurring within a short period rises sharply and nonlinearly. This clustering of jumps reflects the asymmetric dynamics of market liquidity in a crisis state: sudden evaporation and slow recovery.

Directional clustering reveals the asymmetry of volatility clustering. Empirical data show that volatility clustering triggered by price declines significantly exceeds clustering triggered by price increases in both intensity and duration. The root of this asymmetry is that the positive feedback loop of the liquidation mechanism is stronger in a declining market: falling prices erode long-position margin, triggering forced liquidations; liquidation orders act as market sell orders that push prices down further, forming a self-reinforcing downward spiral. By comparison, although short liquidations also occur in a rising market, their systemic positive feedback is typically weaker. This asymmetry stems from three structural factors. First, the share of long open interest in perpetual futures markets is typically higher than that of shorts, so the stock of positions available for liquidation is larger on the downside. Second, long liquidations destroy buy-side purchasing power at the system level (margin is confiscated), whereas the purchasing power released by short liquidations is dispersed across different accounts and is not necessarily reinvested in the market. Third, market makers withdraw liquidity more rapidly in response to downside volatility than to upside volatility, because downside risk typically poses a more direct threat to market makers' inventory.

These empirical facts—tail clustering, jump clustering, and directional clustering—demonstrate that although statistical models can precisely fit the persistence of volatility, they cannot answer the mechanistic question of why the conditional variance depends on past shocks. Moving from "description" to "explanation" requires introducing the causal chain of market microstructure and participant behavior. The next section begins with the outermost slow variables and gradually constructs this causal chain.

## 23.2 Slow variables and the fragility baseline

Beneath the surface appearance of volatility clustering lie complex microstructural dynamics. The framework faces an endogeneity problem at the outset: volatility is both the explained variable and a determinant of the state of the slow variables, since a low-volatility environment itself drives leverage accumulation. This circularity is a common challenge in the analysis of financial systems and can be partly mitigated by introducing indicators exogenous to volatility (such as the ratio of open interest to market capitalization or the number of active on-chain addresses). To understand why high-volatility periods tend to persist, one must decompose the factors that drive market volatility across different time scales. In this analytical framework, the most fundamental level consists of macro and systemic factors that change relatively slowly. These factors, termed "slow variables," do not directly generate instantaneous price jumps, but they constitute the underlying environment in which the market operates and determine how sensitive the market is to external shocks. The mechanism through which slow variables operate is to set the activation threshold of the feedback loops: within a safe range, even a large information shock can be smoothly absorbed by the market; within a dangerous range, a minor disturbance may trigger a violent liquidation cascade and liquidity exhaustion.

### 23.2.1 The macroeconomic environment

The macroeconomic environment is the outermost slow variable that determines the overall tone of crypto-asset markets. As a typical high-beta asset, Bitcoin and other cryptocurrencies exhibit extremely high sensitivity of their volatility to changes in global liquidity conditions and investor risk appetite [9]. The interest rate cycle plays a central role in this transmission mechanism. When a central bank is in a rate-hiking cycle or maintains a high-interest-rate environment, the rise in risk-free yields inevitably depresses global investors' overall risk appetite. Against this macroeconomic backdrop, capital tends to withdraw from the high-risk, high-volatility crypto market, thinning overall market liquidity. A systemic decline in liquidity means that, under an order-flow shock of the same magnitude, asset prices deviate more sharply, thereby raising the baseline volatility level at the macro level [10]. The transmission strength of the interest rate channel to the crypto market is time-varying, however, and may be weaker than commonly assumed. During 2023–2024, BTC still rose sharply even as the Federal Reserve maintained the highest interest rate level in two decades. This counterexample suggests that crypto-native factors, such as ETF inflows and the halving narrative, can override interest rate transmission in particular periods. The macro variable that more directly affects crypto-market liquidity may be the total amount of USD liquidity—including the size of the Federal Reserve's balance sheet and the global M2 supply—rather than the policy rate level itself.

Beyond traditional macroeconomic indicators, the narrative cycles unique to the crypto market constitute another dimension of slow variable. In stages dominated by a bull-market narrative, optimistic market sentiment prompts traders to make widespread use of leverage. Although this sentiment-driven leverage accumulation manifests initially as steady price increases and positive volatility, it in fact accumulates structural fragility within the system. Conversely, in a bear-market narrative, persistent negative expectations lead market makers and arbitrage capital to scale back their operations, and market depth and resilience decline markedly. At this point, any negative news is more likely to trigger a disproportionate price decline in an environment lacking buy-side support, manifesting as strong negative volatility clustering [11].

Macroeconomic uncertainty—such as geopolitical conflict or a sudden shift in inflation expectations—further reinforces this slow-variable effect. When macroeconomic uncertainty rises, cross-market arbitrageurs and macro hedge funds typically reduce their risk exposure in the crypto market. This precautionary withdrawal of capital not only reduces the market's effective liquidity but also raises the risk aversion of all participants. Thus, although changes in the macroeconomic environment unfold slowly on a monthly or quarterly scale, they set the baseline for the low-frequency component of volatility and determine the market's initial resistance when facing sudden events.

### 23.2.2 The level of systemic leverage

In crypto derivatives markets, the level of systemic leverage is the key internal slow variable that determines the intensity of volatility clustering. As the earlier analysis of leverage endogeneity noted, the evolution of leverage over the market cycle is not random but follows a self-reinforcing logic. During a calm period of persistently rising prices, the margin value of existing positions increases accordingly, so the effective leverage ratio naturally declines. This superficial sense of safety prompts traders to establish new leveraged positions or to raise the leverage multiples of existing ones, so that a massive volume of open interest slowly accumulates at the system level.

Figure 23-2 illustrates the nonlinear relationship between the level of systemic leverage and volatility amplification. Leverage does not directly generate volatility; its core role is to define the trigger distance of a liquidation cascade.

![Figure 23-2](./images/fig-23-2-en.png)

**Figure 23-2.** How slow variables set the activation threshold of feedback loops (Drawn by the author based on this chapter's analytical framework; conceptual illustration, not empirical data)

In a high-leverage environment, an initial price decline of merely 2% can reach the liquidation lines of a large number of highly leveraged long positions. Once the liquidation engine is activated, forced market sell orders indiscriminately hit the order book, driving prices down further and, in turn, triggering the liquidation of more positions that were originally in the safe zone [12]. This low trigger threshold, set by the accumulation of leverage, explains why, in certain market states, a trivial piece of external news can trigger volatility as high as 10% or even more extreme. The persistent climb of leverage during a bull market shortens the liquidation trigger distance, so that a minor price disturbance can set off the positive feedback loop of volatility clustering.

### 23.2.3 Liquidity depth

If the level of leverage determines the scale of potential selling pressure, then liquidity depth determines the market's capacity to absorb it. In the crypto market, the baseline level of liquidity is not constant but is constrained by the capital-deployment cycles of professional market makers, constituting a core slow variable. Market makers' capital-allocation decisions are typically based on a long-term risk-return assessment, including funding costs, investment in technical infrastructure, and expectations about overall market trading activity. This adjustment of capital deployment is a slow process, so the market's apparent depth remains relatively stable over weeks or even months.

Changes in liquidity depth directly alter the price impact function. At year-end, during holidays, or in prolonged market downturns, market makers tend to systematically reduce their capital deployment across exchanges, thinning the order book. Against this slow-variable backdrop of scarce liquidity, even routine-scale institutional rebalancing or a moderate information shock can produce far greater price slippage than usual, owing to the lack of sufficient counterparties, which manifests statistically as a rise in volatility [13].

A particularly destabilizing interaction also exists between liquidity depth and the level of systemic leverage. Figure 23-3 reveals how this interaction shapes the market's most fragile state: when high leverage (enormous potential liquidation selling pressure) and thin liquidity (extremely weak absorptive capacity) appear simultaneously, the market enters a highly unstable danger zone in which liquidation orders are more easily triggered and encounter enormous slippage during execution, accelerating the spread of the liquidation cascade [14].

![Figure 23-3](./images/fig-23-3-en.png)

**Figure 23-3.** The two-dimensional fragility surface of the interaction between leverage level and liquidity depth: in the lower-left region (low leverage, ample liquidity) the volatility response is approximately linear, whereas in the upper-right region (high leverage, thin liquidity) the convexity increases sharply (Drawn by the author based on market microstructure theory; conceptual illustration, not empirical data)

The core message of Figure 23-3 is that systemic fragility is not determined linearly by any single slow variable but is driven nonlinearly by the interaction term between leverage level and liquidity depth. This interaction is closer to a threshold interaction than to simple multiplication: when the systemic leverage ratio is below a certain critical level, the effect of liquidity depth on fragility is approximately linear and mild; once the leverage ratio crosses that threshold, the sensitivity of fragility to liquidity increases convexly and sharply, because high leverage shortens the liquidation trigger distance, so that a liquidity gap of the same magnitude causes disproportionate price displacement and liquidation volume. This feature explains why monitoring risk indicators along a single dimension is often insufficient to capture the system's true fragility.

### 23.2.4 The pre-programming of fragility

Taking the macroeconomic environment, leverage level, and liquidity depth together yields a core insight about volatility clustering: slow variables do not directly generate short-term violent volatility; their mechanism is to "pre-program" the market's fragility, thereby determining how low the threshold for activating the feedback loops is. This mechanism can be described as a state-dependent nonlinear response.

During periods when the slow variables are in the safe range—that is, when the macroeconomic environment is accommodative, systemic leverage is moderate, and market-maker liquidity is ample—the market possesses a strong shock-absorbing capacity. At such times, even when major negative news breaks or a large-scale selling shock hits, ample liquidity can smoothly absorb these orders, and the low leverage ratio ensures that a short-term price decline does not trigger a chain of forced liquidations. In this state, the volatility induced by a shock is isolated, its energy decays rapidly, and volatility does not exhibit pronounced clustering.

However, as the slow variables gradually shift into the danger range, the market microstructure undergoes a qualitative change. Using the joint time series of the level of systemic leverage and conditional volatility, Figure 23-4 depicts the complete cycle in which the "fragility gap" widens continuously during the calm period and is then violently released once triggered.

![Figure 23-4](./images/fig-23-4-en.png)

**Figure 23-4.** The time-series relationship between the level of systemic leverage and volatility (Simulated by the author based on leverage-cycle theory; core parameters: α=0.08, β=0.90, with systemic leverage in the figure ranging roughly from 8× to 19×; illustrative simulation, not empirical data)

In this highly fragile state, what triggers a crisis is often not a large-scale black-swan event but merely a routine information shock or a market order slightly larger than usual. This minor disturbance is enough to break through the feedback-activation threshold that the slow variables have already driven to an extremely low level, triggering the liquidation engine and driving market makers to retreat. Once the self-reinforcing cycle of liquidity withdrawal and liquidation selling begins to operate, volatility no longer depends on the input of external information but is self-perpetuated and amplified by the market's internal microstructural mechanisms. Volatility clustering is therefore not a purely random phenomenon but the inevitable result of slow variables gradually accumulating fragility along the time dimension and finally releasing it violently through feedback loops under a minor trigger. The specific path by which slow variables evolve toward the danger range during low-volatility periods is analyzed in detail in Section 23.6.

## 23.3 Positive feedback loops and shock amplification

After slow variables have set the market's fragility baseline, the key factor determining whether volatility clustering actually occurs is the activation of positive feedback loops. This section analyzes three positive feedback channels—between volatility and liquidity, between volatility and leverage, and between volatility and market behavior—to explain how an initial shock produces persistent volatility clustering along the time series through microstructural transmission.

### 23.3.1 The intertemporal transmission of shocks

The analysis in Chapter 22 identified four main sources of volatility: information shocks, liquidity frictions, microstructural mechanisms, and behavioral biases. This cross-sectional perspective explains, at any given moment, which factors jointly push up market price volatility. However, to understand why volatility exhibits pronounced clustering along the time series, one must shift the analytical perspective from a static decomposition of sources to a dynamic time-series evolution. The core of volatility clustering is that an initial external shock not only has an impact in the current period but also, through the market's internal transmission mechanisms, alters the market state of the next period, so that a subsequent shock of the same magnitude can trigger larger price movements.

This time-series self-amplification mechanism constitutes the microfoundation of volatility memory. When an information shock in period t causes violent price movement, market makers contract their liquidity supply because of the rise in inventory risk and adverse-selection risk (the mechanism is detailed in Section 23.3.2), pushing the market liquidity of period t+1 below the normal level. In a liquidity-scarce environment, even if only routine-scale order flow appears in period t+1, it produces a far larger price impact than usual owing to insufficient market depth, thereby realizing higher volatility [15]. This transmission chain clearly explains the microeconomic meaning of the β coefficient in the GARCH model: the conditional variance depends on past shocks because past shocks, by altering the behavior of market participants and the state of the system, substantially reduce the market's capacity to absorb new shocks.

### 23.3.2 The liquidity loop

Among all the mechanisms that amplify volatility, the feedback loop between volatility and liquidity has the shortest transmission path. This loop is essentially the manifestation, along the volatility dimension, of the reflexivity triangle discussed in Chapter 20. The classic model of Kyle (1985) [16] defines the price impact coefficient $\lambda$ as the marginal effect of order flow on price, while the illiquidity measure proposed by Amihud (2002) [17]—the ratio of the absolute value of daily returns to trading value—provides a standardized measure for cross-market liquidity comparison. Both classic indicators require a revised reading in crypto perpetual futures markets, however. The Kyle lambda derives from an equilibrium model of a single risk-neutral market maker facing informed traders, which differs structurally from the crypto environment of multiple competing market makers who can cancel orders at any time; and the Amihud ratio is highly sensitive to the choice of aggregation window (hourly, daily, weekly) in a 24/7 continuous-trading market. In practice, the decay rate of order-book weighted depth—for example, how the ratio of depth in the ±0.5% and ±2% price ranges changes with volatility—may be a liquidity measure more native to perpetual futures. Nevertheless, the core mechanism that the Kyle lambda captures—that the marginal price impact of order flow rises nonlinearly as liquidity declines—still holds in the crypto market. When market volatility rises, $\lambda$ rises nonlinearly, and the cost structure faced by market makers changes nonlinearly. According to inventory models and information-asymmetry theory, market makers' cost function exhibits pronounced convexity when volatility rises [18]. Market makers' liquidity withdrawal unfolds along two causal paths. First, market makers actively widen their quotes and withdraw quoted depth because of the rise in inventory risk and adverse-selection risk; this is a rational response based on a risk-return trade-off. Second, market makers are forced to reduce their exposure because their own margin constraints tighten, and in extreme cases this even triggers the liquidation of the market makers' own positions. In crypto perpetual markets, because market makers bear no obligation to remain present, the response along the first path is extremely fast (millisecond-level order cancellation) and is usually the primary driver of liquidity evaporation. The common result of both paths is that market makers sharply reduce quoted depth across all levels of the order book.

The withdrawal of liquidity has a direct and significant effect on market microstructure. As the order book thins, the price impact coefficient faced by a market order of the same magnitude increases severalfold. During extreme volatility, the bid-ask spread can rapidly widen from a normal 3 basis points to more than 30 basis points, and the market impact coefficient can even be amplified tenfold [19][20]. This large price jump caused by liquidity exhaustion is statistically recorded as a further rise in realized volatility. This rise in secondary volatility contains no new fundamental information; it is purely a mechanical result of the deterioration in market microstructure and the decline in liquidity-bearing capacity. Because the process by which market makers reassess risk and restore liquidity supply is typically slow and cautious, this liquidity-scarce state persists, so the volatility amplification effect continues along the time series and ultimately manifests as the volatility clustering we observe in the data.

The foregoing analysis of the liquidity loop implicitly assumes a single exchange and a single asset, but the actual transmission network is far more complex. BTC perpetual futures trade simultaneously on more than a dozen exchanges, each of which uses a composite index incorporating prices from other platforms as its mark price. When a liquidation cascade on one exchange causes a sharp price drop, its price deviation is transmitted through the index price to other platforms, triggering their liquidations even if their own order books have not been directly hit. Under a unified margin account, losses on a BTC perpetual position can also directly cause margin shortfalls for positions in ETH, SOL, and other instruments within the same account, forcing traders to close out non-BTC instruments to raise liquidity. The cross-market liquidity spiral described by Brunnermeier and Pedersen (2009) [21] is therefore especially pronounced in crypto derivatives markets: during the May 2021 event, the daily correlation between BTC and ETH rose markedly (climbing above 0.9 in the crisis period), a direct manifestation of this cross-instrument contagion.

The liquidity loop does not operate in isolation but is nested with the leverage loop and the behavioral loop. Figure 23-5 integrates these three feedback channels into a unified conceptual network, showing how an initial shock is transmitted simultaneously along multiple paths and reinforced at each node.

![Figure 23-5](./images/fig-23-5-en.png)

**Figure 23-5.** Conceptual diagram of volatility feedback loops (Drawn by the author based on this chapter's analytical framework; conceptual mechanism illustration, not empirical data)

The key feature of Figure 23-5 is that multiple cross-coupling points exist among the three loops. The withdrawal of liquidity simultaneously lowers the execution quality of liquidation orders (coupling with the leverage loop) and intensifies the visual impact of price jumps (coupling with the behavioral loop), while the panic selling of retail investors in the behavioral loop further consumes the already-thin liquidity. This multi-channel, cross-coupled network structure makes the volatility amplification effect far greater than any single loop can explain. The following two subsections analyze the independent transmission mechanisms of the leverage loop and the behavioral loop respectively.

### 23.3.3 The leverage loop

The liquidity feedback loop explains the slow decay of volatility, whereas the leverage feedback loop explains the violent short-term eruption of volatility. In perpetual futures markets, high leverage is not merely a tool of capital efficiency but a core source of systemic fragility. When an initial rise in volatility causes a large deviation in the asset price, the margin balances of traders holding highly leveraged positions are rapidly eroded. As net value declines, the effective leverage ratio of these positions rises passively, bringing them ever closer to the threshold that triggers forced liquidation [22].

This passive rise in effective leverage significantly increases the probability of liquidation across the entire system. Once the price reaches a key liquidation line, the exchange's liquidation engine automatically takes over the position and sends a large volume of market orders to the book. This forced, extremely price-insensitive order flow floods into an already fragile order book, instantly breaking through multiple layers of liquidity and driving a further plunge or spike in price. This violent price movement driven by liquidation generates additional volatility, which in turn triggers deeper liquidations, forming the classic liquidation cascade [14]. This is a positive feedback mechanism whose operation requires no external information input and is driven entirely by the internal leverage-clearing demand of the system. Exchanges have designed multiple circuit-breaker mechanisms to curb this cascade, including tiered margin systems (large accounts face higher margin rates to suppress concentration), auto-deleveraging (ADL) mechanisms (which preferentially offset profitable counterparties rather than dumping everything at market price), and insurance funds (which absorb bankruptcy losses to avoid socialized loss allocation). In extreme conditions, however, these mechanisms often fail to curb the cascade effectively—because the insurance fund is exhausted within minutes, auto-deleveraging triggers panicked withdrawal by counterparties, and tiered margin adjusts with a lag amid successive price gaps—so that positive feedback ultimately still dominates market dynamics. This feedback loop does not terminate naturally until all these circuit-breaker mechanisms have failed, or until leverage has been fully released and fragile positions have been completely unwound. Because a large-scale deleveraging process often requires several consecutive days of liquidation activity to complete, and each day's liquidations create new volatility in the market, the duration of deleveraging overlaps highly, along the time series, with the period of extreme volatility clustering.

### 23.3.4 The behavioral loop

In crypto-asset markets, the high share of retail investors gives the emotional contagion and herd behavior studied in behavioral finance a more prominent role in volatility transmission. When market volatility rises sharply, it is often accompanied by a surge in media coverage and the rapid spread of panic on social networks. This deterioration of the information environment triggers investors' loss aversion and herd mentality, leading large numbers of noise traders lacking fundamental support to flood into the market and engage in panic selling or momentum chasing [23]. This irrational trading behavior not only fails to provide liquidity but consumes precious market depth, further pushing up the market's realized volatility. At the same time, not all retail investors choose to sell in a decline. "Buying the dip" is a deeply entrenched behavioral pattern in the crypto community, and some traders add leverage to buy in as prices fall. Research shows that the loss aversion and aggressive trading behavior of Bitcoin derivatives traders under liquidation risk systematically amplify the tail losses of hedged portfolios in extreme markets [24]. Such behavior can slow the pace of the rise in volatility in the short term, but it ultimately converts these newly established highly leveraged positions into fuel for the next wave of liquidations, making the delayed cascade larger in scale.

At the institutional-investor level, behavioral feedback takes a more institutionalized and mechanical form: the value-at-risk (VaR) spiral. Most institutional investors and market makers are subject to strict VaR risk-control models. When market volatility rises, the VaR value computed from historical data soars accordingly, causing the institution's risk exposure to rapidly approach or breach its internally set risk limit. To meet compliance requirements and internal risk-control standards, these institutions are forced to cut their risk exposure simultaneously—that is, to sell risk assets—precisely when market liquidity is worst. This procyclical de-risking behavior generates enormous selling pressure, directly causing further price declines and a continued rise in volatility, which in turn triggers a new round of VaR breaches and forced liquidations [21]. In practice, only a few leading market makers and hedge funds in the crypto market are truly bound by strict VaR models. A larger share of trading volume comes from retail and semi-professional traders who use simple stop-losses or fixed position limits, and whose de-risking is driven more by a pain threshold than by a model. Nevertheless, whether it is retail panic selling or institutional mechanical de-risking, both reinforce the self-propagation of volatility along different dimensions.

### 23.3.5 Activation and termination conditions

Feedback loops are not activated in every market state; their activation threshold is determined by the slow-variable dynamics of the first layer of explanation (Section 23.2.4). When the slow variables are in the safe range, the threshold is high, and the market can absorb a large information shock without triggering systemic positive feedback; once a high leverage ratio or excessive liquidity concentration has caused fragility to accumulate sufficiently, the threshold drops markedly, and a routine-scale shock is enough to trigger the feedback loops.

Once a feedback loop is activated, its termination exhibits pronounced lag and asymmetry: the end of volatility clustering depends on the exhaustion of the momentum internal to the feedback mechanism, and this exhaustion is far slower than the activation (the bidirectional micro-mechanisms of entering and exiting the high-volatility regime are detailed in Section 23.4.3). The leverage loop must wait for large-scale liquidations to complete and the systemic leverage ratio to fall substantially; the liquidity loop must wait for market makers to return cautiously at a higher risk premium; and the termination of the behavioral loop lags especially. This lag arises not because the same participants gradually become desensitized, but because the price-sensitive seller cohort has already been flushed out during the earlier liquidations and panic. The remaining holders either have already accepted their paper losses (refusing to realize losses under the disposition effect) or are new entrants who built positions at lower prices, so the composition of the market crowd has undergone a structural change. Because capital rebuilding, confidence recovery, and the resetting of risk-control parameters all take time, the termination of a feedback loop is far more protracted than its activation. This explains the sharp-rise, slow-decay asymmetric shape of volatility clusters in real data. This asymmetry also reveals a structural blind spot of the standard GARCH model: its β coefficient imposes a symmetric decay structure on upward and downward shocks, which systematically underestimates the speed of the transition from calm to crisis while overestimating the speed of recovery from crisis to calm. Asymmetric GARCH variants—such as the GJR-GARCH proposed by Glosten, Jagannathan, and Runkle (1993) or the EGARCH—can better capture this dynamic [25], which will be discussed further in the selection of volatility forecasting models in Chapter 24.

## 23.4 The state machine and volatility regime transitions

The interaction between slow variables and feedback loops makes volatility change not continuously and smoothly but with discrete state jumps. Although continuous GARCH-type models can fit the persistence of volatility, they cannot capture the market's abrupt shifts between calm and crisis. This section introduces a Markov regime-switching model that abstracts the volatility dynamics of perpetual futures markets into nonlinear transitions among three discrete states—calm, stressed, and crisis—and analyzes the asymmetry of state transitions and their interaction with slow variables.

### 23.4.1 The model framework

In traditional financial econometrics, volatility clustering is usually modeled as a continuously evolving process. The GARCH model and its variants form the foundation of this analytical paradigm, whose core assumption is that the conditional variance at the current moment is a continuous function of past return shocks and past variances. Within this framework, volatility slides smoothly between "high" and "low," and its response to new information takes the form of a gradual adjustment of variance. However, the empirical data of cryptocurrency perpetual futures markets reveal a markedly different dynamic character: changes in volatility are often not continuous but exhibit pronounced jumpiness and state-like behavior. The market may hold a low annualized volatility of 30% for weeks, then jump above 120% within hours on a single liquidation event, *sit* at this high level for several days, and then switch states again. This multimodal feature in the frequency distribution suggests that a single continuous process is insufficient to capture the abrupt changes in market microstructure; volatility in fact switches among several discrete regimes [7].

To describe this nonlinear regime switching precisely, the Markov regime-switching model provides a rigorous statistical framework. Hamilton (1989) [26] first introduced the Markov chain into the analysis of macroeconomic time series, proposing that the generating process of an observed variable depends on an unobservable discrete state variable. When this idea is extended to volatility modeling, it forms the Markov regime-switching conditional-heteroskedasticity model [27][28]. In this model, the market is assumed to be in one of a finite number of discrete states, each with its own mean, variance characteristics, and mechanism for responding to shocks. Let the unobservable state variable $S_t \in \{1, 2, 3\}$ correspond to the three states of calm, stressed, and crisis, respectively, with transitions among states governed by a $3 \times 3$ transition probability matrix $\mathbf{P}$:

$$\mathbf{P} = \begin{pmatrix} p_{11} & p_{12} & p_{13} \\ p_{21} & p_{22} & p_{23} \\ p_{31} & p_{32} & p_{33} \end{pmatrix}$$

where $p_{ij} = \operatorname{Pr}(S_t = j \mid S_{t-1} = i)$, and the elements of each row sum to 1. The conditional return distribution in each state follows a normal distribution with different parameters:

$$r_t \mid S_t = k \sim \mathcal{N}(\mu_k, \sigma_k^2), \quad k = 1, 2, 3$$

where $\sigma_1^2 < \sigma_2^2 < \sigma_3^2$, corresponding to the increasing conditional variances in the calm, stressed, and crisis states. Throughout this chapter, the volatility metric is realized volatility (returns aggregated intraday at a 5-minute frequency), annualized by the crypto-market convention of continuous trading 365 days a year—that is, the daily volatility is multiplied by $\sqrt{365}$—rather than the traditional-market convention of $\sqrt{252}$. The current state depends only on the previous state, which is precisely the core embodiment of the Markov property. By introducing discrete states, the model can explain why in some periods the market has an extremely high capacity to absorb shocks, while in other periods a shock of the same magnitude triggers a violent surge in volatility.

Applying the Markov regime-switching model to perpetual futures markets rests intuitively on the nonlinear mapping between the continuous change of slow variables and the threshold activation of feedback loops. Slow variables such as macro liquidity depth and the systemic leverage ratio undergo slow and continuous evolution in daily trading, and these changes do not by themselves directly manifest as a rise in volatility. However, the feedback loops in the microstructure—particularly the liquidation cascade and the market-maker order-cancellation mechanism—have a distinct threshold-trigger character. When the accumulation of slow variables pushes systemic fragility past a certain critical point, an ordinary information shock that could originally have been smoothly absorbed instantly activates the positive feedback loop. Once the feedback loop is activated, the market microstructure undergoes a qualitative change, and the system "jumps" from one state into an entirely new one. In the new state, high-frequency liquidation events and widened bid-ask spreads reinforce each other, allowing the market to sustain itself within this high-volatility regime until the internal imbalance is fully digested. This discrete jump, driven by continuous slow variables and triggered via a threshold mechanism, constitutes the third layer of explanation for understanding volatility clustering in perpetual futures.

### 23.4.2 The transition matrix

Based on empirical estimation with a hidden Markov model (HMM), the volatility dynamics of perpetual futures markets can be abstracted into a three-state Markov machine: the calm state, the stressed state, and the crisis state. The three-state division is a deliberate simplification of the actual market continuum. The internal risk-control systems of major exchanges typically use a finer-grained classification of five to six market states (including intermediate states such as early warning and price-protection triggering); this chapter adopts three states to strike a balance between analytical simplicity and the ability to capture the phenomenon. These three states differ significantly not only in their statistical distributions but also in the relative weights of their underlying microscopic drivers. The calm state is the market's norm, occupying roughly 65% to 75% of trading time. In this state, annualized volatility typically remains in the range of 20% to 40%, and the return distribution is approximately normal with thin tails. The microstructure is characterized by extremely narrow bid-ask spreads, liquidation volume at a trough, and smoothly functioning cross-exchange arbitrage. At this point, volatility is driven mainly by exogenous information shocks, with information sources accounting for more than 60% of total volatility, and traditional continuous volatility models have good predictive power in this regime.

When market fragility accumulates and a specific shock strikes, the system jumps to the stressed state, which accounts for about 20% to 30% of the time. The stressed state is typically characterized by annualized volatility rising to 50% to 80%, with the return distribution beginning to show pronounced fat tails and skewness. At the microscopic level, market makers perceive increased risk and begin to passively widen spreads and reduce order-book depth; at the same time, some highly leveraged positions approach the liquidation line, causing liquidation volume to rise initially. In this regime, the contributions of liquidity sources and mechanistic sources (such as funding-rate pulses) to volatility increase significantly, together accounting for 40% to 60%. If the shock is not relieved and liquidation volume breaks through a critical threshold, the market moves further into the crisis state. Although the crisis state accounts for only 3% to 8% of total time, its annualized volatility often soars above 100% to 200%, accompanied by extreme fat tails and frequent price jumps. At this point, the liquidation cascade erupts fully, liquidity is nearly exhausted, mechanistic sources completely dominate market dynamics, and the relative importance of information shocks falls to its lowest level.

Figure 23-6 integrates these three states and their transition logic into a complete state-machine schematic.

![Figure 23-6](./images/fig-23-6-en.png)

**Figure 23-6.** Schematic of the volatility state-transition machine for perpetual futures (Drawn by the author based on a Markov regime-switching model [26]; the transition probabilities and time shares are the author's HMM estimates on daily data for Binance BTC-USDT perpetual futures from 2019 to 2024, with wide confidence intervals, not empirically measured)

Two key structural features can be identified intuitively from Figure 23-6. First, the self-loop probability of the calm state (the probability of remaining in the current state) is the highest, indicating that the low-volatility regime has the strongest capacity for self-maintenance. Second, the probabilities of the two paths departing from the stressed state (regression toward calm and deterioration toward crisis) are not far apart, which means that the stressed state is a highly uncertain bifurcation point whose ultimate direction depends on the specific configuration of the slow variables at that moment.

Transitions between states are not a random walk but follow a specific set of empirical probability matrices. According to the HMM parameter estimates on historical high-frequency data (the following ranges are based on the same HMM parameter estimates listed in the figure note above), the daily probability of the market jumping from the calm state to the stressed state is typically between 2% and 5%; once in the stressed state, the probability of further deterioration to the crisis state rises significantly, reaching 5% to 15%. This means that the stressed state is a highly unstable transitional period that either evolves rapidly into a full-blown crisis or returns to calm after turbulence. The probability of regression from the crisis state to the stressed state is relatively high, at about 15% to 30%, reflecting the fact that extreme liquidation events typically exhaust their momentum within a few days; however, the probability of complete regression from the stressed state to the calm state is only 10% to 20%. This parameter structure of the transition matrix indicates that the calm state has the strongest regime stickiness, with an expected dwell time of 20 to 50 days, whereas the crisis state has the shortest expected dwell time, typically only 3 to 7 days, though the microstructural damage it causes is prolonged through a longer stressed state.

The state-machine parameters above are estimated from daily data on a single trading pair (Binance BTC-USDT perpetual) and have three limitations. First, a single-pair model cannot capture state transitions transmitted from other exchanges or other assets; for example, the 2022 FTX collapse first hit FTT and SOL before being transmitted to BTC perpetual futures. Second, daily data may mask state transitions at the intraday microstructural level: a trading day classified as "calm" by a daily-frequency model may contain a localized crisis at the 15-minute level (such as a flash crash followed by rapid recovery). Third, the effective number of observations for some state-condition combinations (such as the low-liquidity range within the stressed state) is limited, so the confidence intervals of the transition-probability estimates may be wide. Multi-exchange joint HMM estimation or extended estimation on hourly data can mitigate these limitations to some extent, but this is beyond the scope of this chapter.

### 23.4.3 Transition asymmetry

In the three-state volatility model, a prominent dynamic feature is the pronounced asymmetry of state transitions: the market enters a high-volatility regime far faster than it exits one. Empirical data show that falling from the calm state, through the stressed state, fully into the crisis state often takes only 1 to 3 days, and in extreme cases the jump can be completed within hours; whereas cooling down from the crisis state, through the stressed state, and finally returning to a truly calm state typically requires a repair period of 5 to 20 days or even longer. This large difference in time scale is what gives volatility clusters their sawtooth shape—sharp rise, slow decay—on time-series charts.

By contrasting the typical time paths of entering and exiting the high-volatility state, Figure 23-7 illustrates this asymmetry intuitively.

![Figure 23-7](./images/fig-23-7-en.png)

**Figure 23-7.** Comparison of the temporal asymmetry of volatility state transitions (Drawn by the author based on this chapter's analytical framework; conceptual illustration, not empirical data)

This macro-statistical asymmetry is rooted in the asymmetry of the behavioral patterns of micro-level market participants and of mechanism design. Entering a high-volatility state is usually initiated by a single triggering event. When an information shock exceeding expectations strikes a fragile market that has already accumulated high leverage and thin liquidity, it immediately triggers the automated liquidation engine. The high-leverage nature of perpetual futures causes liquidation orders to hit the order book as market orders regardless of cost, instantly draining buy-side or sell-side liquidity. This algorithmically forced selling is not constrained by human hesitation or wishful thinking, and its transmission speed is limited only by the processing capacity of the exchange's matching engine. At the same time, once market makers' risk-control models detect the jump in volatility and the loss of control over inventory risk, they automatically cancel orders or sharply widen spreads at millisecond speed. The positive feedback of automated liquidation and the instantaneous withdrawal of machine market makers superimpose on each other, so that the market completes its jump to the crisis state in an extremely short time.

By contrast, exiting a high-volatility state is a protracted process involving the psychological reconstruction of multiple parties and the redeployment of capital. First, although the liquidation cascade in the crisis state is fierce, it must wait for excessively leveraged positions to be fully and *naturally digested*, and this deleveraging process takes time to find a new price equilibrium. Second, after experiencing extreme volatility, market makers' VaR models significantly raise their expectations of future volatility, causing them to exercise great caution when resupplying liquidity. Redeploying capital must pass through reassessment and approval by risk-control departments, and market makers typically return tentatively and gradually with wider spreads and smaller sizes, rather than restoring liquidity depth to pre-crisis levels all at once. Finally, the emotional recovery of market participants likewise exhibits a lag effect: the memory of panic brought by extreme volatility causes traders to lower their leverage and reduce their trading frequency for a considerable period. These slow micro-level repair mechanisms jointly determine that the regression from a high-volatility regime to a low-volatility regime must be a gradual, repeatedly interrupted decay process.

### 23.4.4 The regulation by slow variables

Although the Markov regime-switching model provides an elegant framework for describing the discrete jumps of volatility, treating the transition-probability matrix as a fixed constant would ignore deeper market dynamics. In fact, the state machine does not operate in isolation in a vacuum; its internal transition probabilities are time-varying, and what determines these dynamic changes in probability is precisely the "slow variables" described in the first layer of explanation. The three major slow variables—the macroeconomic environment, the level of systemic leverage, and liquidity depth—constitute the underlying physical environment in which the state machine operates, and by regulating the sensitivity of the microscopic feedback loops, they directly determine the specific values of the individual elements of the transition matrix.

The level of systemic leverage is the most critical slow variable determining the transition probability from the calm state to the stressed state. During a prolonged calm period, the low-volatility environment entices traders to continually raise their leverage multiples in pursuit of capital efficiency, causing the system's overall effective leverage ratio to climb gradually. Once a high-leverage environment has formed, the market's tolerance for adverse price movement drops sharply. At this point, a minor information shock that would originally have been insufficient to cause a ripple can reach the liquidation lines of a large number of highly leveraged positions. Therefore, as the systemic leverage ratio rises, the transition probability from the calm state to the stressed state increases sharply and nonlinearly. High leverage lowers the market's tolerance for price disturbances to an extremely low level, so that a routine-scale information shock can trigger a liquidation cascade.

Liquidity depth and macroeconomic uncertainty mainly determine the probability of deterioration from the stressed state to the crisis state. When market-maker capital deployment is insufficient or the market is in a specific low-liquidity holiday period, the absorptive capacity of the order book is extremely fragile. In such a thin-liquidity environment, once the market enters the stressed state and an initial liquidation flow appears, the lack of sufficient counter-liquidity to absorb it causes prices to shift disproportionately and violently, rapidly triggering a larger-scale liquidation cascade. Empirical research shows that during periods when liquidity depth is in the bottom historical quartile, the probability of the market sliding from the stressed state into the crisis state is more than three times that of liquidity-ample periods (this multiple is based on a conditional HMM estimate on the aforementioned Binance BTC-USDT perpetual daily data: after grouping order-book depth by historical quartile, the state-transition matrix of each group is fitted separately, and the inter-group difference in the stressed-to-crisis transition probability is compared; because the number of joint observations with the stressed state and liquidity in Q1 is limited, the 95% confidence interval of this multiple estimate is wide, at approximately 2.1 to 4.8 times, and it should be regarded as an order-of-magnitude indication rather than a precise parameter). At the same time, if the macroeconomic environment is in a high-interest-rate or high-uncertainty cycle, the overall risk appetite for risk assets is suppressed, and all transition probabilities toward high-volatility states are systematically amplified [29]. It is precisely this deep interaction between slow variables and state-transition probabilities that explains why the intensity and frequency of volatility clustering in perpetual futures markets vary significantly across different macro and micro market cycles.

## 23.5 The institutional amplifiers of perpetual futures

The preceding three sections established the three-layer explanation in turn: slow variables set the fragility baseline, feedback loops amplify shocks, and the state machine drives regime jumps. However, these mechanisms may exist in any leveraged derivatives market; the reason perpetual futures markets exhibit clustering intensity far exceeding that of traditional markets lies in the systematic amplification that their distinctive institutional design imposes on these three layers. The institutional features are not themselves independent sources of volatility; each of their core components enhances the clustering effect by lowering the feedback-activation threshold or accelerating the feedback transmission speed. This directly explains why the clustering intensity of perpetual futures observed in Section 23.1 is so much higher than in traditional financial markets. The three institutional features—the liquidation engine, funding rates, and around-the-clock trading—together construct an almost frictionless transmission environment, and their synergistic amplification logic is drawn together in Section 23.5.4.

### 23.5.1 Funding rates

The funding rate is a periodic payment mechanism designed for perpetual futures to maintain the anchoring of the contract price to the spot price (as described in Chapter 10). By design, the funding rate is first of all a convergence mechanism: by charging the deviating side and paying the reverting side, it incentivizes arbitrageurs to enter and correct the deviation, effectively suppressing excessive deviation between the contract price and the spot price in most market states. However, when the market is in a strong one-sided trend and volatility rises sharply, arbitrageurs cannot maintain opposing positions because they face extremely high liquidation risk, the rate's convergence function fails, and the mechanism flips from a stabilizer into an amplifier. The critical condition for this flip corresponds roughly to the funding rate remaining at an extreme value in the same direction for several consecutive settlement periods (for example, exceeding 0.1% for three consecutive 8-hour periods). In the context of volatility clustering, once the flip occurs, the funding rate amplifies the trend within a trend and amplifies volatility at turning points, becoming an endogenous positive feedback engine. In the calm state, the funding-rate pulse is minuscule and its effect on volatility is negligible; in the stressed or crisis state, however, an extreme rate significantly prolongs the duration of high volatility. The crypto spot-futures basis (carry) has been shown to embed amplification dynamics related to crash risk [30].

In a strong one-sided market, the positive feedback loop of the funding rate is especially evident. When long forces dominate the market, the contract price generates a premium, and the funding rate turns positive. In theory, a positive rate should incentivize shorts to enter and arbitrage, thereby depressing the price; but in the high-volatility state of a bull market, shorting faces extremely high liquidation risk, and shorts struggle to maintain positions. The result is that longs continue to accumulate, prices rise further, the funding rate is pushed to a higher level, and this instead attracts more momentum-chasing speculators. When the market finally reverses, the destructive power of the feedback loop is released instantly. The funding rate swings sharply from an extreme positive value to negative, and the longs that had enjoyed the trend dividend begin to be penalized and are forced to close positions. The closing of long positions drives prices down, further deepening the negative shift of the funding rate, prompting more longs to be forced to close, and ultimately triggering a liquidation cascade.

Figure 23-8 shows the synchronization between funding-rate pulses and volatility clustering: during the market's transition from calm to crisis, the arbitrage-closing behavior triggered by extreme rates translates directly into additional directional volatility, giving volatility stronger persistence.

![Figure 23-8](./images/fig-23-8-en.png)

**Figure 23-8.** The linkage between funding-rate pulses and realized volatility (Representative illustration, synthetic series, not empirical data; the funding-rate axis in the figure is a synthetically amplified series that only illustrates its synchronization with volatility, not the true magnitude of the rate—the true perpetual rate is approximately 0.1%–0.3% per 8 hours, see main text; the volatility × leverage × liquidity framework mechanism is based on a crypto-market derivatives analysis report [31])

This pulse-superposition effect of the funding rate manifests in quantitative models as a higher persistence parameter in the GARCH model. Naimy et al. (2021) showed that, in capturing the volatility clustering characteristics of cryptocurrencies, a GARCH model incorporating asymmetric effects better reflects this mechanism-driven volatility jump, with a persistence parameter significantly higher than in traditional fiat-currency markets [9].

### 23.5.2 Automated liquidation

The core difference in margin mechanisms between traditional futures markets and perpetual futures lies in the execution speed of liquidation. In traditional delivery futures, when an account's margin is insufficient, the exchange issues a margin call, and the trader typically has a T+1 time window to add funds or close the position independently. This design provides a buffer for the market: liquidation is dispersed, and different traders respond at different points in time. Perpetual futures, by contrast, use an automated liquidation engine: when the mark price reaches the bankruptcy price, the engine immediately takes over the position and liquidates it at market price, with no manual intervention at any point, and the mark price is monitored at millisecond frequency. From trigger detection to the generation of the liquidation order, this process is indeed completed on a millisecond scale; however, the actual execution of the liquidation order—that is, filling level by level on the order book until the position is fully closed—may last several seconds or longer in extreme markets, because the rapid evaporation of order-book depth forces the liquidation order to seek counterparties at ever more distant price levels. When large numbers of liquidations are triggered simultaneously, the matching engine may become congested or even degrade (for example, in May 2021 the latency of Binance's matching engine spiked to the second level), forming a "liquidation cliff" effect: after the engine recovers, the backlog of liquidation orders is released all at once, causing a price impact far greater than under continuous processing.

This speed difference fundamentally alters the transmission dynamics of volatility. In perpetual futures, liquidation is synchronous and concentrated. The engine simultaneously processes all triggered leveraged positions, and the concentrated liquidation flow directly hits the order book. Because market makers typically widen spreads and withdraw liquidity during high volatility, the order book's absorptive capacity is at its weakest. The liquidation flow creates a deeper price dip in the thin order book, and this new price low immediately triggers the next batch of originally safe positions, forming the classic liquidation cascade.

Using a scatter plot of 24-hour cumulative liquidation volume against contemporaneous realized volatility, Figure 23-9 reflects the positive feedback relationship between the two: the scatter exhibits pronounced nonlinearity, and once liquidation volume breaks through a critical level, the volatility response steepens sharply.

![Figure 23-9](./images/fig-23-9-en.png)

**Figure 23-9.** The positive feedback effect between 24-hour liquidation volume and realized volatility (Representative scatter illustration, synthetic series, not empirical data; mechanism based on a crypto-market derivatives analysis report [31])

In perpetual futures, leverage routinely reaches 100×, and superimposed on an instantaneous liquidation mechanism it gives the positive feedback an extremely high gain. The liquidation volume triggered by a 3% price decline in perpetual futures may be several times that in traditional futures markets. This additional volatility manufactured by the liquidation engine accumulates along the time series and directly causes deep volatility clustering. The liquidation cascade not only creates extreme volatility in the current period but also lays the foundation for high volatility in subsequent periods by thoroughly destroying the liquidity structure. The operational risk of the liquidation engine itself also constitutes an independent amplification channel: when engine overload causes liquidation delays, positions not liquidated in time continue to lose money and accumulate bankruptcy losses, ultimately triggering the exhaustion of the insurance fund and auto-deleveraging; the latter forcibly closes the positions of profitable counterparties, so that even traders who correctly predicted the direction are forced out of the market, further contracting liquidity. The regulatory evolution surrounding liquidation mechanisms is accelerating: for example, the European Union's MiCA framework imposes orderly-operation and risk-management requirements on crypto-asset service providers; some jurisdictions (such as Hong Kong) set caps on retail clients' virtual-asset leverage exposure; and several common-law jurisdictions have begun to examine whether automated liquidation under a manipulated mark price constitutes unfair trading conduct. If these regulatory interventions are fully implemented, they will fundamentally reshape the transmission dynamics of liquidation cascades.

### 23.5.3 Around-the-clock trading

Traditional financial markets have fixed closing times and weekend market closures. This design objectively acts as a systemic shock absorber. During the market close, market makers have time to reassess risk models and deploy capital, traders can calmly digest information, and algorithmic logic can be manually reviewed. Overnight information shocks are typically reflected as a one-time gap at the next day's open, rather than triggering continuous feedback transmission during the session.

Perpetual futures markets operate around-the-clock, continuous trading, which means the feedback loops are always in an activatable state. Information shocks can be transmitted at any point in time, especially during late-night or weekend hours when liquidity is naturally thin. In these low-liquidity windows, an order-flow shock of the same magnitude produces far greater price movement than during normal hours. Once volatility triggers the liquidation engine or an extreme value of the funding rate, the feedback loop operates continuously in an environment lacking sufficient liquidity buffer.

This continuous-trading mechanism facilitates the cross-time-zone relay transmission of volatility. Volatility originating in the Asian trading session may continue to be amplified in the European session because of insufficient liquidity, and then trigger a larger-scale leverage clearing in the American session. Volatility clustering can therefore cross the closing boundaries of traditional markets, forming high-volatility clusters lasting days or even weeks. The profound impact of around-the-clock trading on market microstructure has attracted wide attention, with related analyses noting that low-liquidity periods such as weekends and late nights have become high-incidence windows for volatility eruptions [32]; traditional exchanges such as CME have also begun to launch around-the-clock crypto derivatives trading. While amplifying volatility, 24/7 trading also has a mitigating side: continuous trading eliminates the overnight gaps of traditional markets and allows information to be incorporated into prices more smoothly along the timeline; major exchanges have also deployed circuit-breaker-like mechanisms such as price-protection bands and extreme-market trading limits to partly compensate for the systemic fragility of having no market close, though the effectiveness of these mechanisms in extreme markets remains to be verified. Low-liquidity windows also invite strategic exploitation. In *liquidation hunting*, a trader places large directional orders during the thinnest-liquidity periods to trigger a cascade and profit from the resulting dislocation, which makes the fragility of these windows not merely a passive structural feature but an active, adversarial amplification mechanism.

### 23.5.4 Synergistic effects

The directional amplification of funding rates, the speed amplification of the automated liquidation engine, and the temporal amplification of around-the-clock trading—these three institutional features work together to make the volatility clustering intensity of perpetual futures systematically higher than in traditional markets. Figure 23-10 lays out how the three synergistically reinforce volatility clustering.

![Figure 23-10](./images/fig-23-10-en.png)

**Figure 23-10.** The conceptual transmission path of perpetual futures volatility amplifiers (Drawn by the author based on this chapter's analytical framework; conceptual mechanism illustration, not empirical data)

The transmission path in Figure 23-10 reveals the hierarchical relationship among the three amplifiers: the funding rate amplifies the trend and accumulates one-sided positions along the directional dimension, the automated liquidation engine instantaneously converts the fragility of positions into a market-price impact along the speed dimension, and around-the-clock trading eliminates the window for the system to cool naturally along the time dimension. The superposition of the three is not a simple linear summation but exhibits a multiplicative relationship: the larger the one-sided positions accumulated by the funding rate, the more violent the impact released when the liquidation engine is triggered, and around-the-clock trading ensures that this impact can be detonated during the most fragile periods, such as the thinnest-liquidity late-night Asian hours. This "direction × speed × time" multiplicative effect is a heuristic description rather than a strict independent-factor model; strong coupling exists among the three amplifiers (24/7 trading allows funding rates to accumulate continuously, and extreme rates in turn trigger more liquidations), so the actual amplification factor may be higher than the simple product of the three. In addition, the analysis above focuses on the institutional design of centralized exchanges; on-chain order-book decentralized exchanges (DEXs), such as Hyperliquid and dYdX v4, face different but equally significant amplification mechanisms: the block-time constraint limits the liquidation-processing capacity per unit of time, the centralized single-point dependence of the sequencer may become a bottleneck under high load, and the update latency of the price oracle may cause a systematic deviation between the liquidation trigger and the true market price.

Returning to the cross-market comparison data in Table 23-1, the persistence parameter of perpetual futures is systematically higher than in traditional futures and spot markets, its shock-decay speed is the slowest, and its volatility half-life is the longest. The GARCH persistence parameter of traditional fiat-currency pairs is typically markedly lower than that of crypto perpetual futures, with a shorter volatility half-life and a shorter duration of extreme clustering episodes (the author's synthesis of multi-source estimates: fiat persistence of about 0.90–0.95, half-life of about 5–15 days, and clustering episodes of about 1–4 days); this directional difference is consistent with the empirical conclusions of [9].

The extreme volatility-of-volatility observed in perpetual futures markets does not stem from the intrinsic properties of the underlying asset but is the inevitable result of institutional design. If the automated liquidation engine were removed or trading circuit breakers introduced, the intensity of volatility clustering would decline structurally. This conclusion has important policy and design implications: in assessing and managing systemic risk in crypto markets, risk-control models cannot rest on the statistical extrapolation of historical volatility alone but must treat the nonlinear transmission logic of these institutional amplifiers as a core consideration.

## 23.6 The accumulation of fragility during low-volatility periods

In cryptocurrency perpetual futures markets, a prolonged low-volatility environment is often misinterpreted by market participants as a signal of reduced risk. From the perspective of system dynamics, however, this calm is not true safety but a process in which fragility accumulates covertly within the system. When the market remains in a low-volatility state for an extended period, the behavioral responses of traders, the market-making strategies of liquidity providers, and the parameter updates of risk-management models jointly constitute a self-reinforcing fragility-production mechanism. This mechanism explains why the most intense volatility clusters in cryptocurrency markets often erupt right after the longest calm periods. This section examines the endogenous evolution of leverage and liquidity during low-volatility periods, traces the microscopic chain through which stability produces instability, and shows how the pattern appears in empirical data.

### 23.6.1 The endogenous accumulation of leverage

In the financial instability hypothesis, Minsky pointed out that the stable periods of a capitalist economy endogenously breed instability, because prolonged stability induces market participants to take on greater risk [33]. Minsky's theoretical framework divides the financial cycle into three stages: the hedge-financing stage (participants can repay debt through cash flow), the speculative-financing stage (participants can only repay interest but must borrow anew to repay principal), and the Ponzi-financing stage (participants cannot even repay interest and rely entirely on rising asset prices). Perpetual futures trading in cryptocurrency markets is an accelerated version of this evolution, and the low-volatility period is precisely the critical transition from hedge financing to speculative financing. However, the gradual deterioration from hedge financing to Ponzi financing in Minsky's framework depends on the relationship between debt-servicing cash flow and income, whereas perpetual futures trading does not generate "income" in the traditional sense, and participants' solvency depends entirely on the direction of asset-price movement. In this sense, highly leveraged directional perpetual futures positions have the characteristics of speculative or Ponzi financing from the moment they are opened, and Minsky's gradual-deterioration narrative is better understood in the crypto context as the accumulation process of total systemic leverage rather than a stage-by-stage evolution in the nature of financing. Geanakoplos's (2010) [34] leverage-cycle theory—whose core thesis is that changes in collateral value endogenously alter credit availability and produce procyclical fluctuations in leverage—may provide a theoretical anchor more directly applicable to crypto derivatives markets. This theory is especially pronounced in cryptocurrency perpetual futures markets, and its evolution is far faster than in traditional macroeconomic cycles. In the participant structure of cryptocurrency markets, the share of retail investors is far higher than in traditional financial markets, and retail investors' risk perception is often based on recent market performance rather than on long-run statistical regularities. When asset-price volatility remains low for a prolonged period, the behavioral patterns of market participants undergo a systematic change, and this change directly leads to a covert climb in the system's overall leverage level.

The starting point of the behavioral response is the interaction between risk perception and risk-management models. In a low-volatility environment, a VaR model estimated from historical data outputs extremely low risk assessments [35]. For institutional investors, this means that under the same risk budget, they can and must allocate a larger notional position to maintain the target rate of return. For individual traders, prolonged sideways movement or slow appreciation significantly lowers their vigilance toward tail risk, prompting them to adopt higher leverage multiples in perpetual futures. Over time, the ratio of the entire market's open-interest value to spot market capitalization continuously climbs. This phenomenon is especially pronounced in cryptocurrency markets, because the leverage caps of perpetual futures are often far higher than in traditional futures markets (BTC perpetual futures on some exchanges can reach 100× leverage or higher), and retail investors, with relatively weak risk awareness, are more likely to adopt extreme leverage driven by the false sense of safety of low volatility.

This leverage-accumulation process is further amplified under the funding-rate mechanism unique to perpetual futures. When the market is in a calm period with a slight long bias, the funding rate tends to remain stable and positive. This stable income stream attracts a large number of arbitrageurs into the market to establish basis-arbitrage or funding-rate-arbitrage positions. Although these arbitrage positions are market-neutral by design, they greatly increase the total open interest of the perpetual futures market. At the same time, these seemingly low-risk positions are equally subject to maintenance-margin requirements when the market state changes abruptly. The distinction matters. Funding-rate arbitrage positions are delta-neutral by design—a spot long against a perpetual short—and their risk comes not from directional losses but from the margin calls caused by basis jumps and from the liquidity risk that the spot leg cannot be closed in time in extreme markets. Therefore, arbitrage open interest (OI) and speculative OI contribute to systemic fragility in different ways. In assessing systemic risk, the share of speculative OI is a more informative indicator than total OI. Nevertheless, when the calm period is broken and volatility rises sharply, both speculative and arbitrage positions of enormous size face margin pressure, instantly converting into potential liquidation momentum and providing ample fuel for subsequent volatility clustering.

At the microscopic level, leverage accumulation during low-volatility periods is also reflected in the dynamic adjustment of exchanges' margin systems. Exchange margin adjustment is in fact the superposition of multiple layers of mechanism: volatility-linked dynamic margin (procyclical—that is, lowering requirements when volatility is low, encouraging leverage), position-size tiered margin (countercyclical—that is, large accounts face higher margin rates, suppressing concentration), and, on some exchanges, pre-announced adjustment (buffering—that is, granting a 24-to-48-hour preparation period). On regulated exchanges (such as CME), margin adjustment is constrained by notice-period requirements, and its procyclical effect is buffered; on offshore exchanges, zero-notice margin adjustment can itself become a trigger of volatility. The net effect of the three remains procyclically dominated, because volatility-linked dynamic margin has the widest coverage and the largest adjustment magnitude. During low-volatility periods, dynamic margin requirements are gradually lowered, which further incentivizes traders to adopt higher leverage. Overall, this procyclically dominated margin-adjustment system is itself a fragility-amplification mechanism: when volatility suddenly rises, exchanges are often forced to rapidly raise margin requirements, and this sudden change in requirements triggers the forced liquidation of large numbers of positions, thereby intensifying the rise in volatility.

In extreme cases, exchanges may even suspend the liquidation function when market volatility rises to an extreme, in order to prevent a system collapse. Although this "circuit breaker" mechanism protects the exchange's system stability in the short term, it simultaneously freezes the market's price-discovery mechanism, so that trapped positions cannot be closed at any price, further intensifying the panic of market participants. This phenomenon was fully demonstrated in the "Black Thursday" event of March 2020, when the liquidation systems of several exchanges were temporarily paralyzed by excessive traffic, leaving large numbers of positions unable to be closed in time and ultimately causing greater losses. On-chain liquidation systems exposed a different but equally serious fragility in the same event: MakerDAO's on-chain liquidation auctions were nearly paralyzed by severe congestion on the Ethereum network, as liquidators could not submit bid transactions because of the surge in gas fees, causing large amounts of collateral to be filled at zero bids. The fragility of on-chain liquidation stems from the throughput bottleneck of the underlying network rather than a design flaw in the liquidation engine itself, and it constitutes an amplification mechanism physically entirely different from the overload of a centralized exchange (CEX) liquidation engine.

### 23.6.2 Liquidity concentration

Accompanying the covert rise in leverage is a profound distortion of the liquidity structure. During low-volatility periods, market makers face a markedly different competitive environment and risk-return trade-off. Because prices fluctuate within a narrow range, orders far from the current market price have an extremely low probability of being executed, which greatly reduces the capital efficiency of providing liquidity across a wide price range. To capture limited trading volume and maximize capital utilization amid fierce competition, market makers rationally adjust their quoting strategy.

The core manifestation of this adjustment is the extreme concentration of liquidity. Market makers deploy the vast majority of their capital in an extremely narrow range hugging the current best bid and ask, compressing the bid-ask spread to the extreme and making the order book's apparent depth near the price appear exceptionally ample [36]. This surface abundance, however, masks the structural emptiness deeper in the order book. Because capital is drawn tightly toward the touchline, depth far from the current price declines sharply. In automated market maker (AMM) mechanisms, the widespread adoption of concentrated-liquidity design likewise intensifies this phenomenon, as liquidity providers tend to concentrate their funds near the current price to earn the highest fee income.

This distortion of the liquidity distribution greatly increases the fragility of the system. During calm periods, the extremely narrow spread and ample touchline depth create for traders an illusion of excellent market liquidity. However, once an information shock beyond ordinary expectations or a large sell order appears, the liquidity concentrated near the touchline is instantly broken through. Because far-end depth is empty, price jumps sharply as it searches for the next level of liquidity support. This discontinuous jump, triggered by a liquidity fault, produces a price impact far greater than under a normal liquidity distribution, pushing the system directly from a low-volatility state into an extreme high-volatility state within a very short time.

From the perspective of data microstructure, this phenomenon can be quantified through the shape parameters of the order book. During low-volatility periods, the order book typically exhibits a "spiked" shape—that is, an extremely high depth density near the current price, but a sharp decline in depth as the price distance increases. By comparison, the order-book shape under normal market conditions is more uniform and gradual. This spiking not only reduces static shock-absorption capacity but also weakens the order book's recovery resilience—that is, the speed at which the order book returns to its pre-shock state after a price impact. Bouchaud et al. (2009) [37] showed that liquidity gaps in the order book amplify the price impact of a single order, and that the spread and depth recovery after a shock follow a slow power-law decay; this "slow recovery" feature corresponds directly to the "slow termination" feature of the liquidity loop described in Section 23.3. When the market shifts from calm to volatile, this spiked-shape order book cannot effectively absorb large order flow, forcing prices to jump to more distant price levels to find sufficient liquidity. In this process, each price jump triggers more liquidations, which in turn causes more sell orders to flood in, forming a self-reinforcing vicious cycle.

### 23.6.3 Empirical relationships

The "calm trap" is not merely a theoretical deduction but an empirical regularity deeply imprinted in the historical data of cryptocurrency markets. The evolution of slow variables (such as the leverage level and the liquidity structure) takes time; the longer a calm period lasts, the deeper these slow variables slide toward the danger range and the greater the fragility the system accumulates. A significant positive correlation therefore exists between the length of a calm period and the intensity of the volatility cluster that subsequently erupts.

Observation of Bitcoin's historical market movements clearly reveals this pattern. For example, before the violent crash of the Bitcoin price in mid-November 2018, the market experienced months of extremely low volatility, during which the Bollinger Bands narrowed to a historical extreme and open interest continuously climbed. Likewise, before the extreme "Black Thursday" market of March 2020, the market had also gone through a relatively calm, optimistic period. The May 2021 crash followed the same pattern: in the preceding weeks, Bitcoin oscillated repeatedly within the $45,000 to $65,000 range, volatility remained at a low level, yet open interest kept increasing. These historical events show that the eruption of extreme volatility clustering is often not an isolated random event but the inevitable result of continuously accumulating fragility during a long calm period.

Figure 23-11 shows the scatter relationship, based on Bitcoin historical data, between the length of calm periods and the intensity of subsequent volatility clustering: low-volatility calm periods lasting more than 50 days are often accompanied by subsequent extreme volatility clusters whose annualized volatility peaks exceed 100%, confirming that time is a key dimension of fragility accumulation. To quantify this relationship, defining a calm period as a continuous period in which the 30-day realized volatility is below an annualized 35%, and defining clustering intensity as the peak of the 30-day realized volatility that follows, the author identified about 15 independent calm-period–eruption-period pairs in BTC historical data from 2018 to 2024. The Spearman rank correlation coefficient is approximately 0.72 (N=15, p<0.01), though under such a small sample its confidence interval is wide (the 95% confidence interval is approximately 0.35 to 0.90), and removing the single most extreme event (March 2020) reduces the rank correlation to about 0.60. Although the precise value of the point estimate is sensitive to sample composition, the direction of the positive correlation remains robust across various calm-period definition thresholds (25% to 45%) and volatility measures, indicating statistically meaningful support for the explanatory power of calm-period length over subsequent clustering intensity.

![Figure 23-11](./images/fig-23-11-en.png)

**Figure 23-11.** The positive correlation between calm-period length and subsequent volatility clustering intensity in Bitcoin historical data (Illustrative: direction of positive correlation; the author's proprietary sample of BTC from 2018 to 2024, not independently verified, not a precise estimate)

The mechanism behind this empirical relationship lies in the time-accumulation property of slow variables. The accumulation of leverage, the concentration of liquidity, and the parameter drift of risk models do not happen instantaneously but evolve slowly, day by day and week by week, during the calm period. A 30-day calm period may accumulate only enough fragility to support 50% volatility clustering, whereas a 70-day calm period may accumulate enough to support 150% volatility clustering. This nonlinear relationship explains why certain relatively small triggering events can provoke extreme market reactions after a long calm period.

### 23.6.4 Early-warning signals

Once the mechanism of fragility accumulation during low-volatility periods is understood, the core of risk management shifts from "predicting when a shock will occur" to "assessing how fragile the current system is." The VIX paradox in traditional financial markets points out that when the volatility index is at its lowest, it is often the moment when hedging demand is weakest and the system is least protected, and at this point the market's endogenous fragility is in fact highest [38]. In cryptocurrency perpetual futures markets, although a volatility-derivatives market of equal depth is lacking, we can identify the "calm trap" through a set of observable microstructural indicators.

In fragility assessment, leverage indicators are at the most upstream point of the causal chain. The ratio of the notional value of open interest to the market capitalization of the underlying asset is the most intuitive indicator of systemic leverage. In a low-volatility environment, if this ratio shows a persistent upward trend accompanied by the funding rate long deviating from a neutral level, it strongly suggests that a large number of highly leveraged positions extremely sensitive to one-directional price movement are accumulating in the market. Figure 23-12 simulates the entire process in which open interest gradually climbs during the calm period, converts into liquidation momentum that pushes up volatility after the turning point, and then falls rapidly during the liquidation cascade—a process typically completed within hours to days.

![Figure 23-12](./images/fig-23-12-en.png)

**Figure 23-12.** The temporal evolution dynamics of open interest and volatility in perpetual futures (Simulated by the author based on leverage-cycle theory; illustrative simulation, not empirical data)

Leverage accumulation determines the potential liquidation momentum, but whether this momentum can be absorbed by the market depends on the distribution structure of liquidity. Simply observing the touchline spread is often deceptive, because the extremely narrow spread of a low-volatility period is precisely the result of excessive liquidity concentration. A more reliable early-warning signal is the concentration indicator of order-book depth—that is, the ratio of quoted volume near the touchline (for example, within a 0.5% range) to quoted volume in a wider range (for example, within a 2% or 5% range). If this ratio rises significantly during a low-volatility period, it indicates that liquidity is becoming extremely concentrated, far-end depth is being hollowed out, and the market's capacity to absorb unexpected shocks is declining sharply. When this ratio exceeds 150% of the historical median, the system has already entered a high-fragility state. However, the depth-concentration ratio based on order-book snapshots has inherent limitations: visible quotes contain a large number of non-committed quotes (such as the ghost liquidity described in Chapter 20) that are rapidly withdrawn when the market moves, so the indicator may overestimate true depth. Alternative indicators based on actual transaction data—such as the time-weighted average price impact or the VPIN (volume-synchronized probability of informed trading) indicator—are less susceptible to illusory liquidity and can serve as cross-validation tools. More fundamentally, the early-warning indicators above have so far only been validated in-sample, and their out-of-sample predictive power (particularly sensitivity and specificity) still needs to be established through testing over a longer time series before operable early-warning thresholds can be set.

Above the objective fragility of the system constituted by leverage and liquidity, behavioral and sentiment indicators reflect market participants' subjective cognitive bias toward this fragility. The extremization of the retail long-short ratio, the persistent exuberance of social-media sentiment indicators, and the narrowing of the spread between market makers' quoted implied volatility and historical realized volatility all indicate that market participants severely underprice tail risk. During low-volatility periods, if the spread between implied and realized volatility (commonly called the "volatility premium") remains persistently negative with a continuously expanding absolute value, this indicates that the market is collectively underestimating risk. This cognitive bias in turn reinforces leverage accumulation, because participants who underestimate risk are more inclined to raise their leverage multiples. Microstructural indicators such as the directionality of order flow, the arrival frequency of large orders, and market makers' inventory levels can further verify the above trends: when the arrival frequency of large buy orders persistently exceeds that of large sell orders during a low-volatility period, this suggests that market participants are actively building leveraged long positions.

Figure 23-13 summarizes the complete transmission mechanism of fragility accumulation during low-volatility periods. These early-warning signals cannot predict the timing and nature of the triggering event, but they can assess the system's current level of fragility, thereby shifting the focus of risk management from "when it will happen" to "how severe it will be if it happens."

![Figure 23-13](./images/fig-23-13-en.png)

**Figure 23-13.** The mechanism of fragility accumulation and abrupt state change in a low-volatility environment (Drawn by the author based on this chapter's analytical framework; conceptual mechanism illustration, not empirical data)

The transmission path in Figure 23-13 clearly displays the complete logical closed loop of the "calm trap." Starting from the low-volatility environment at the top, three paths—leverage accumulation, liquidity concentration, and risk underestimation—advance in parallel, jointly pushing the system toward a high-fragility critical state. When an external triggering event breaks through the activation threshold set by the slow variables, the system jumps sharply from the upper part of the figure (the slow-accumulation stage) to the lower part (the rapid-release stage), and the positive feedback loop of liquidation cascade and liquidity exhaustion causes volatility to surge to extreme levels within a short time. The practical significance of this path diagram is that risk managers should focus their attention on the three accumulation paths in the middle of the figure, because they are the observable, measurable early-warning dimensions.

## 23.7 Case study: the life cycle of the May 2021 crash

To validate the three-layer explanatory framework of "slow variables → feedback loops → state machine" proposed above, we need a real market case with a complete life cycle. The Bitcoin market crash of May 2021 provides a classic natural experiment. This event was not a single random shock but a demonstration of the complete dynamic process of how volatility gradually accumulates fragility from a low level, how it is sharply amplified by positive feedback loops after a triggering event, and how the market state rapidly jumps from calm to crisis. By dissecting this historical case, we can clearly see how microstructural mechanisms shape the macro phenomenon of volatility clustering.

### 23.7.1 The state of the slow variables

The cryptocurrency market in the first quarter of 2021 was in a typical "calm" state, but this surface stability masked a sharp rise in underlying systemic fragility. The evolution of the slow variables set the tone for the subsequent violent volatility.

The level of systemic leverage, as the primary slow variable, underwent unprecedented expansion during this period. The Bitcoin price climbed from $29,000 at the start of 2021 to $64,000 by mid-April, a gain of more than 120%. In this strong uptrend, the endogenous character of leverage was fully displayed: as prices rose, the effective leverage ratio of long positions passively declined, prompting traders to continually add new leverage to maintain their target risk exposure. According to whole-market BTC perpetual futures data aggregated by Coinglass (including coin-margined and USDT-margined contracts), the notional value of open interest surged from about $10 billion at the start of 2021 to about $27 billion by mid-April, and climbed further to a peak of about $28 billion before the May crash [39]. At the same time, this leverage expansion was accompanied by extremely skewed market sentiment, with the funding rate long remaining at a level of 0.1% to 0.3% per 8-hour settlement period (a simple annualization of about 110% to 330%, though because arbitrageurs typically build positions when rates are low, the actual cost borne during the holding period is lower than the simple annualized value), indicating that longs not only held absolute dominance but were also willing to pay a high cost to maintain leverage.

Liquidity depth, another slow variable, was likewise gradually changing for the worse. Although the number of surface quotes on the order book appeared ample when prices were high, market makers' capital deployment exhibited a highly concentrated character. A large amount of liquidity clustered within an extremely narrow range near the current price, while the deep order book far from the current price was abnormally empty. This liquidity structure meant that once the price broke through the narrow high-liquidity range, the market would face a liquidity-fault zone with almost no buffer [20].

At the same time, changes in the participant structure further intensified the system's fragility. Blockchain data analysis shows that during this period the vast majority of Bitcoin addresses were in an unrealized-profit state, and large numbers of newly entered retail investors had established highly leveraged long positions at high prices [40]. These inexperienced investors had extremely low tolerance for price fluctuations, and their stop-loss orders were densely distributed not far below the current price. From the perspective of behavioral finance, the disposition effect (Shefrin & Statman 1985 [41]) meant that the large number of unrealized-profit holders constituted an enormous pool of potential sellers—profitable holders tend to close positions within the profit range; once a negative catalyst appeared, this seller pool could be rapidly activated, triggering large-scale profit-taking selling.

By this point, the slow variables had completed a dangerous combined configuration: elevated systemic leverage, weak deep liquidity, and highly concentrated stop-loss orders. This state of "high leverage + thin depth + high sentiment" constituted an extremely fragile market environment. In such an environment, the system did not need to withstand a large-scale external shock; a routine-scale piece of negative news was enough to break through the feedback-activation threshold that the slow variables had lowered to an extremely low level.

### 23.7.2 The trigger and initial shock

In mid-May 2021, the long-accumulated fragility finally met its triggering event. This trigger was not a single catastrophic piece of news but the superposition of a series of negative events that together broke through the critical point at which the system maintained equilibrium.

On May 12, Tesla CEO Elon Musk announced on social media that, out of concern about the environmental impact of Bitcoin mining, Tesla would stop accepting Bitcoin as a means of payment [42]. This statement directly struck one of the core narratives underpinning the first-quarter bull market—institutional adoption. Immediately afterward, on May 13, Chinese regulators reiterated their ban on financial institutions and payment companies providing cryptocurrency-related services, further intensifying market panic. Such regulatory shocks amplify and spread risk through the contagion channel between crypto assets and traditional securities markets [43]. Unlike a one-time information shock such as the Musk tweet, the Chinese regulatory tightening was essentially a structural institutional change; it not only triggered panic in the short term but also, over the medium to long term, set off a series of structural adjustments—including mining migration, the shift of exchange users to offshore platforms, and the closure of fiat on-ramps—and these supply-side changes lasting for months prolonged the tail of the volatility clustering.

These pieces of news constituted the initial information shock. The Bitcoin price fell at one point in mid-May from about $57,000 to near $52,000, a single-day decline of about 9%. In a traditional spot market, a 9% decline, though significant, would typically be regarded as a normal correction. In the highly leveraged environment of perpetual futures, however, this initial shock underwent a qualitative change.

The initial price decline first caused a sharp reversal in the funding rate. The positive funding rate that had long remained high rapidly turned negative, marking a sudden reversal of market sentiment, and some highly leveraged longs began to be forced to close positions. At the same time, the 9% decline was enough to reach the maintenance-margin lines of a large number of highly leveraged long positions established above $55,000. Initial liquidations began to occur, and the market sell orders automatically generated by the liquidation engine began to hit the order book.

At this stage, the market state machine underwent its first discrete jump: from the "calm" state to the "stressed" state. Volatility indicators responded immediately to this jump, with Bitcoin's realized volatility jumping rapidly from the calm-period range of an annualized 30% to 45% to a level of an annualized 75% to 85%. Market makers began to sense the risk, spreads widened from a normal 3 basis points, and some ghost liquidity (as described in Chapter 20, referring to non-committed market-making quotes that are displayed under normal market conditions but rapidly withdrawn under stress) began to retreat. At this point, however, the system was still in a state of strained support, and a full-blown cascade had not yet erupted.

### 23.7.3 The cascade and crisis

After the initial shock pushed prices down and triggered the first wave of liquidations, the second-layer mechanism—the feedback loops—was fully activated. From May 13 to 19, the market witnessed one of the most violent liquidation cascades in cryptocurrency history, precisely the result of the mutual reinforcement of the volatility-leverage feedback loop and the volatility-liquidity feedback loop.

As prices fell further, the volatility-leverage feedback loop began to operate continuously. Falling prices eroded the margin of more long positions, the effective leverage ratio rose passively, and the liquidation trigger distance shortened. When the price broke below the key psychological threshold of $50,000, it triggered densely distributed stop-loss orders and liquidation orders. These forced sell orders hit the market indiscriminately, driving prices down further and, in turn, triggering deeper liquidations [12].

At the same time, the volatility-liquidity feedback loop intensified this process. Facing sharply rising volatility and one-directional liquidation selling pressure, market makers faced extremely high adverse-selection risk and inventory risk. To protect their own capital, market makers sharply widened the bid-ask spread and even withdrew buy orders entirely. At the most extreme moment, market depth evaporated and the order book became extremely thin [20]. The exhaustion of liquidity meant that the same quantity of liquidation sell orders caused a far larger price impact than usual.

These two feedback loops formed a self-reinforcing downward spiral: liquidation triggered → price decline → liquidity withdrawal → price impact amplified → more positions liquidated. This process peaked on May 19. That day, the Bitcoin price plunged by about 32% within less than 12 hours (an intraday-peak measure; about −30% on a daily-close basis), touching a low below $30,000; Ethereum's decline was deeper, with an intraday maximum drop of about 46% [44].

The data clearly record the severity of this crisis. According to statistics from several data-aggregation platforms (Coinglass, The Block), the notional value of positions forcibly liquidated across the entire crypto market on May 19 exceeded $8 billion (about $8.6 billion by multi-source aggregation; this figure is the notional size of liquidated positions rather than the actual loss amount, the latter being difficult to estimate precisely because of slippage and bankruptcy); among them, Deribit alone saw 296 Ethereum positions and 609 Bitcoin positions undergo bankruptcy liquidation [44]. Whole-market BTC perpetual open interest plunged from about $28 billion to near $10 billion within just a few days, indicating that leverage within the system was violently cleared out [39].

At this stage, the market state machine completed its second jump: from the "stressed" state fully into the "crisis" state. Volatility was no longer continuous but exhibited jump-like behavior, soaring directly from around an annualized 80% to an extreme level of an annualized 150% to 200%. Cross-exchange spreads widened sharply, and the arbitrage mechanism temporarily failed in the face of an extremely congested network and exhausted capital. The cross-instrument contagion effect of this crisis was equally significant: Ethereum perpetual futures plunged 46% on the same day, a decline far exceeding BTC's 32%. This difference may stem from the ETH market's higher starting leverage ratio and thinner deep liquidity, as well as traders under a unified margin account preferentially liquidating the more liquid ETH positions to free up BTC margin. At the peak of liquidation, the insurance funds of several exchanges suffered large drawdowns, and some platforms triggered the auto-deleveraging mechanism (the reverse cascade described in Section 23.5.2, which forcibly closes profitable counterparties' positions), further compressing the supply of liquidity.

Figure 23-14 superimposes four time series from this life cycle—the price trajectory, 24-hour liquidation volume, open-interest size, and realized volatility—so that the reader can trace, on a single timeline, the successive activation and transmission of each layer of mechanism.

![Figure 23-14](./images/fig-23-14-en.png)

**Figure 23-14.** The volatility clustering life cycle of the May 2021 BTC crash (Empirical figure; price and liquidation-volume data sources: Chainalysis [40] and Deribit Insights [44]; open-interest series source: Coinglass [39]; realized volatility is the author's calculation based on daily returns; ETH's intraday maximum drop of about 46% is an intraday-peak measure, about −40% on a daily-close basis)

In Figure 23-14, the three stages corresponding to Sections 23.7.1–23.7.3—incubation, stress, and crisis—can be clearly identified: open interest first climbs to a peak during the calm period, then declines off a cliff during the crisis period, while liquidation volume and realized volatility surge synchronously to extreme values on May 19. The violent movements of the four curves are highly synchronized on the timeline, precisely mapping the positive-feedback transmission path of liquidation cascade → liquidity exhaustion → volatility surge.

### 23.7.4 Theoretical validation

The May 2021 crash case provides a consistent illustration of the three-layer explanatory framework proposed in this chapter, demonstrating the framework's structural advantages in explaining extreme market behavior. The ex-post analysis of a single case carries inherent methodological limitations, however: selective interpretation after the fact may exaggerate the framework's explanatory power, and the framework's applicability to other historical events, such as the 2022 LUNA/UST collapse, still requires independent validation. The discussion that follows should be read under this constraint.

First, the analysis at the slow-variable level successfully explains why the system was in an extremely fragile state before the shock. Traditional statistical models (such as GARCH) can only make lagged adjustments after volatility has already risen and cannot warn of the accumulation of fragility during the calm period. By observing the expansion of open interest and the persistently elevated funding rate, the slow-variable framework accurately captured the potential of "how severe the reaction would be if a shock occurred." This proves that the crisis was not caused unilaterally by Musk's tweet or the regulatory news alone but was the joint result of an extremely fragile environment and an ordinary information shock.

Second, the analysis at the feedback-loop level explains why volatility exhibits clustering and persistence. In the flash crash of May 19, the plunge in price far exceeded what any fundamental information could explain. The closed loop formed by the liquidation engine's mechanical selling and market makers' liquidity withdrawal clearly demonstrates how the shock was self-amplified by the system's internal mechanisms. It is precisely these microstructural feedback loops that constitute the physical basis of the "long memory" in the volatility time series, allowing the high-volatility state to sustain itself for several days after being triggered.

Finally, the state-machine model accurately describes the nonlinear character of market dynamics. The case shows that the transition from "calm" to "stressed" was relatively gradual, but the jump from "stressed" to "crisis" erupted within a few hours. In the crisis state, the dominant source of volatility switched completely from fundamental information to mechanistic liquidation and the absence of liquidity. This asymmetry of state transitions—very fast entry into crisis, slow exit from it—is the fundamental reason volatility clusters in perpetual futures markets display a sawtooth distribution [45].

However, this case also reveals the inherent limitations of the theoretical framework. Although the three-layer framework can accurately assess the system's fragility and explain the amplification mechanism of the feedback loops, it cannot predict the specific timing, nature, and exact magnitude of the triggering event. This limitation does not diminish the framework's value; rather, it points to the correct path for risk management: rather than trying to predict unpredictable triggering events, it is better to focus on monitoring and managing the observable slow variables and feedback states.

Abstracting the causal chain distilled from this case one step further, one can construct a systemic-crisis formation-path model applicable to more general situations. Figure 23-15 decomposes this path into four progressive stages: preconditions, the trigger layer, the transmission layer, and the amplification layer.

![Figure 23-15](./images/fig-23-15-en.png)

**Figure 23-15.** The formation path of a systemic financial crisis (Drawn by the author based on this chapter's analytical framework; conceptual mechanism illustration, not empirical data)

Figure 23-15 expresses this chapter's "slow variables → feedback loops → state machine" framework as a structured path and precisely maps the nonlinear dynamics observed in the May 2021 cryptocurrency market crash: a crisis is not triggered by a single external shock but is the inevitable result of the interaction between the long-term accumulation of internal systemic fragility and specific triggering conditions.

Along this path: in the precondition stage, the evolution of slow variables raises the system's fragility baseline, with the 20× to 100× leverage of perpetual futures acting here as a significant amplifier that raises the system's sensitivity to minor price changes exponentially; in the trigger layer, an exogenous shock shatters the illusion of low volatility and reaches the maintenance-margin lines of a large number of long positions, triggering initial liquidations; the transmission layer corresponds to the state machine's state switching, as the market jumps rapidly from calm to crisis and cross-market contagion and liquidity exhaustion appear in succession; and the amplification layer is the macro-network resonance of the feedback loops, in which the positive feedback of volatility-leverage and volatility-liquidity intertwines and self-reinforces, ultimately evolving local volatility into a full-blown systemic crisis. The policy implication of this formation path is that although a systemic crisis is abrupt, the accumulation of its underlying fragility and the evolution of its transmission mechanisms are traceable, structured processes: through continuous monitoring of the slow variables and feedback states, regulators and market participants may be able to identify the system's critical state before a crisis fully erupts, and thereby adopt more forward-looking risk-management measures.

## 23.8 Chapter summary

In empirical data, volatility clustering manifests as the dependence of the conditional variance on past shocks, a phenomenon that has been widely documented in time-series analysis. However, purely statistical models cannot explain the microscopic source of this memory effect. The three-layer explanatory framework proposed in this chapter fills this theoretical gap, reducing the phenomenon of volatility clustering to an identifiable process of market microstructure evolution. The first layer is the slow variables, including the macroeconomic environment, the level of systemic leverage, and liquidity depth; these variables evolve over longer time scales, and their core role is not to directly generate volatility but to set the baseline fragility for the entire system, determining how high or low the threshold for activating the feedback loops is. The second layer is the feedback loops, which constitute the microscopic dynamic basis for the self-amplification of shocks: significant positive feedback mechanisms exist between volatility and liquidity, leverage, and market behavior, and when an initial shock crosses the activation threshold set by the slow variables, market makers' withdrawal thins liquidity while the erosion of margin triggers passive leverage increases and liquidations—the rational reactions of these micro-agents converge at the macro level into the self-perpetuation of volatility. The third layer is the state-machine model, which discretizes the market's evolution into three states—calm, stressed, and crisis—with transitions among the different states exhibiting strong asymmetry: the process of entering a crisis is often driven by positive feedback and completed within an extremely short time, whereas exiting a crisis requires waiting for the momentum of the feedback loops to be exhausted and for liquidity to recover slowly. Figure 23-16 shows the overall structure of this framework.

![Figure 23-16](./images/fig-23-16-en.png)

**Figure 23-16.** The mechanistic explanatory framework for volatility clustering (Drawn by the author based on this chapter's analytical framework; conceptual framework illustration, not empirical data)

Figure 23-16 condenses the core argumentative structure of this chapter into a bottom-up three-layer architecture diagram. The practical value of this framework is that it provides a layered diagnostic tool for volatility forecasting and risk management: first assess the range in which the slow variables lie to judge systemic fragility; next monitor the activation signals of the feedback loops to identify the precursors of state transitions; and finally select the corresponding forecasting model and hedging strategy according to the current state.

Compared with traditional financial markets, crypto-asset perpetual futures markets exhibit a more violent volatility clustering effect, and this difference stems not from higher uncertainty in the intrinsic value of the underlying asset but from amplification by the market's distinctive institutional design. The liquidation cascade mechanism, under conditions of extremely high leverage and the absence of a margin-call buffer, instantly converts adverse price movements into market-price liquidation orders, producing an extremely high positive-feedback gain. The pulse-superposition effect of funding rates prolongs the duration of high volatility in the stressed or crisis state. The around-the-clock, no-close trading rule eliminates the window for market-maker capital resetting and emotional cooling that the market-close periods of traditional markets provide. To reduce the systemic risk of this market, policymaking and protocol design must intervene in these institutional features—for example, by introducing smoother liquidation-execution algorithms or setting dynamic caps on funding rates. These suggestions are better understood as directions for optimization at the protocol-design level than as top-down regulatory requirements, because trading volume in perpetual futures markets is concentrated mainly on offshore exchanges beyond the reach of most regulators, and globally unified mandatory rules are difficult to achieve in the short term. In addition, if a funding-rate cap is set improperly, it may introduce new distortions: persistent rate suppression would cause a systematic deviation between the contract price and the spot price, or drive trading activity to migrate to platforms without caps, producing regulatory arbitrage.

Low-volatility periods are usually intuitively regarded as safe periods for the market, but this chapter's analysis reveals that they are in essence the stage in which systemic fragility accumulates fastest. During a prolonged calm state, traders gradually raise leverage as confidence strengthens, market makers narrow spreads amid competition and cause liquidity concentration to rise, and the system's overall risk exposure continuously increases—even though all observable volatility indicators are at low levels. This mechanism poses a fundamental challenge to the traditional risk-management paradigm: a VaR model based on historical volatility systematically underestimates tail risk during calm periods. For example, in the calm period before the May 2021 event, the 99% VaR estimated from the past 30 days' realized volatility was about a single-day decline of 8% to 10%, whereas the actual single-day decline on May 19 reached 32%, more than three times the VaR prediction; even switching the risk measure to expected shortfall would struggle to close this gap, because the nonlinear amplification effect of the liquidation cascade exceeds the capture range of any static risk model based on the extrapolation of historical distributions. Therefore, the focus of risk management must shift from merely monitoring the current volatility level to continuously assessing the system's underlying fragility, integrating real-time monitoring of the leverage distribution, liquidity depth, and order-book concentration.

By deconstructing the microstructural mechanisms of volatility clustering, this chapter has answered the core question of why a high-volatility state self-perpetuates. Having clarified the driving mechanisms, the focus of the analysis will turn to how to exploit these regularities. The three-layer framework directly leads to a layered forecasting and decision-making system: first, identify the current market state through observable slow variables and microstructural indicators; next, select the corresponding forecasting model according to the dominant volatility dynamics of each state; and finally, formulate dynamic trading and hedging strategies based on the state-specific path of risk evolution. This logical progression—from mechanistic understanding to quantitative forecasting and then to strategy execution—constitutes the core thread of the next stage of analysis.

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