Liquidation with Self-Exciting Price Impact

Abstract

We study optimal execution with "self-exciting" price impact, where persistent trades not only incur price impact but also increase the execution costs for successive orders. This model is motivated by an equilibrium between fundamental sellers, market makers, and end users. For risk-neutral investors, it leads to faster initial trading compared to the constant execution rate of Bertsimas and Lo (1998). For risk-averse liquidation as in Almgren and Chriss (1999, 2001) or Huberman and Stanzl (2005), self-excitement has a moderating effect: slow liquidation is sped up, whereas fast schedules are slowed down.

Keywords: optimal liquidation, price impact, self-excitement, risk aversion

JEL Classification: G11