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.

中文翻译：

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内生性流动性危机

经验数据显示，流入订单簿的流动性（存款、取消和市价订单）受过去价格变化的影响。特别是，我们表明流动性趋于随着过去波动率和价格趋势的幅度而减少。这种反馈机制反过来会增加波动性，可能导致流动性危机。考虑到程式化订单模型中的这种影响，我们通过数值证明了弱反馈的稳定机制到强反馈的不稳定机制之间存在二阶相变，其中流动性危机的发生概率为 1。我们描述了临界指数，它们似乎属于一个新的普遍性类别。然后，我们提出了一个更简单的价差动态模型，该模型映射到线性霍克斯过程，该过程也表现出流动性危机。如果与实际市场相关，这种相变场景要求系统位于不稳定阈值以下，但非常接近不稳定阈值（自组织临界性），否则反馈强度本身是时间相关的，偶尔会访问不稳定区域。另一种情况是由一类非线性霍克斯过程提供的，它显示偶尔“激活”的流动性危机，而不必在不稳定的边缘徘徊。