Endogenous liquidity crises

Abstract

Empirical data reveals that the liquidity flow into the order book (limit orders, cancellations and market orders) is influenced by past price changes. In particular, we show that liquidity tends to decrease with the amplitude of past volatility and price trends. Such a feedback mechanism in turn increases the volatility, possibly leading to a liquidity crisis. Accounting for such effects within a stylized order book model, we demonstrate numerically that there exists a second order phase transition between a stable regime for weak feedback to an unstable regime for strong feedback, in which liquidity crises arise with probability one. We characterize the critical exponents, which appear to belong to a new universality class. We then propose a simpler model for spread dynamics that maps onto a linear Hawkes process which also exhibits liquidity crises. If relevant for the real markets, such a phase transition scenario requires the system to sit below, but very close to the instability threshold (self-organised criticality), or else that the feedback intensity is itself time dependent and occasionally visits the unstable region. An alternative scenario is provided by a class of non-linear Hawkes process that show occasional ‘activated’ liquidity crises, without having to be poised at the edge of instability.

Classification of flash crashes using the Hawkes(p,q)framework

“…For example in the recently proposed jumpdiffusion model of Bates (2019), large market movements are the result of the accumulation of rapid and self-exciting intraday increases in conditional volatility, a quantity closely related to the conditional intensity of price changes used to describe the price process in the sequel of this paper. A recent study in Fosset et al (2020) further links the occurrence of liquidity crises to such endogenous feedback effects and finds that, for these events to occur, financial markets must either constantly operate just below criticality, or exhibit time-dependent endogenous dynamics that occasionally visit the critical regime in order to produce the events in question. Resonating with the latter scenario and tying back to the argument of approximating aggregate agent behavior using Hawkes processes, also in agent-based models, the parameter controlling the social coupling/herding strength of traders must be allowed to intermittently reach the critical regime in order to reproduce stylized facts of financial markets like volatility clustering, realistic bubbles and corrections (Kaizoji et al 2015, Westphal and.…”

Self-Organized Criticality in Economic Fluctuations: The Age of Maturity

“…A thorough discussion of the potential role played by the SOC state in explaining market microstructure liquidity dynamics is given in Ref. [23]. In classical critical phenomena, universality finds its explanation in the simple observation that macroscopic (aggregate) properties will depend only on the stochastic limiting properties of a model that are not removed by a progressive integration (averaging) of micro-fluctuations.…”

Radical Complexity

“…Such a feedback loop can actually be included in stochastic order book models (such as the now commonly used family of “Hawkes processes” [ 30 ]). As the strength of the feedback increases, one finds a phase transition between a stable market and a market prone to spontaneous liquidity crises , even in the absence of exogenous shocks or news [ 31 ].…”