Dynamic optimal execution in a mixed-market-impact Hawkes price model

TL;DR

This paper derives explicit optimal trading strategies in a linear price impact model with order flows modeled by Poisson or Hawkes processes, analyzing market stability and manipulation potential.

Contribution

It provides a closed-form solution for optimal execution strategies considering Hawkes process-driven order flows, highlighting conditions that prevent price manipulation and promote market stability.

Findings

Poisson order flows enable robust price manipulation strategies.

Hawkes process conditions can prevent manipulation and stabilize markets.

Explicit formulas for optimal trading strategies are derived.

Abstract

We study a linear price impact model including other liquidity takers, whose flow of orders either follows a Poisson or a Hawkes process. The optimal execution problem is solved explicitly in this context, and the closed-formula optimal strategy describes in particular how one should react to the orders of other traders. This result enables us to discuss the viability of the market. It is shown that Poissonian arrivals of orders lead to quite robust Price Manipulation Strategies in the sense of Huberman and Stanzl. Instead, a particular set of conditions on the Hawkes model balances the self-excitation of the order flow with the resilience of the price, excludes Price Manipulation Strategies and gives some market stability.