Self-exciting price impact via negative resilience in stochastic order books

TL;DR

This paper explores the effects of negative resilience in stochastic limit order book models, revealing new qualitative behaviors in optimal trade execution driven by self-exciting price impacts.

Contribution

It introduces a framework allowing negative resilience in stochastic order books, highlighting novel effects on optimal trading strategies compared to traditional positive resilience models.

Findings

Negative resilience models exhibit self-exciting price impact behavior.

Optimal trade execution strategies are significantly affected by negative resilience.

Stochastic market depth and resilience lead to new qualitative effects in trading strategies.

Abstract

Most of the existing literature on optimal trade execution in limit order book models assumes that resilience is positive. But negative resilience also has a natural interpretation, as it models self-exciting behaviour of the price impact, where trading activities of the large investor stimulate other market participants to trade in the same direction. In the paper we discuss several new qualitative effects on optimal trade execution that arise when we allow resilience to take negative values. We do this in a framework where both market depth and resilience are stochastic processes.