Endogenous Liquidity Crises

TL;DR

This paper investigates how feedback mechanisms between past price volatility and liquidity flow can lead to liquidity crises, demonstrating a phase transition in stylized models and proposing simpler Hawkes process models to explain such phenomena.

Contribution

It introduces a stylized order book model showing a second order phase transition to liquidity crises and proposes simplified Hawkes process models capturing similar dynamics.

Findings

Liquidity decreases with past volatility and trends.

A second order phase transition exists between stable and unstable regimes.

Hawkes process models can reproduce liquidity crises.

Abstract

Empirical data reveals that the liquidity flow into the order book (depositions, cancellations andmarket orders) is influenced by past price changes. In particular, we show that liquidity tends todecrease with the amplitude of past volatility and price trends. Such a feedback mechanism inturn increases the volatility, possibly leading to a liquidity crisis. Accounting for such effects withina stylized order book model, we demonstrate numerically that there exists a second order phasetransition 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, whichappear to belong to a new universality class. We then propose a simpler model for spread dynamicsthat maps onto a linear Hawkes process which also exhibits liquidity crises. If relevant for thereal markets, such a phase transition scenario requires the system to sit below, but very close tothe instability threshold (self-organised criticality), or else that the feedback intensity is itself timedependent and occasionally visits the unstable region. An alternative scenario is provided by a classof non-linear Hawkes process that show occasional "activated" liquidity crises, without having to bepoised at the edge of instability.