29 septembre 2022, 11h00–12h15
Salle Auditorium 5
Empirical data reveals that the liquidity flow into the order book is influenced by past price changes. In particular, 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. 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.