Optimal order execution under price impact: A hybrid model

TL;DR

This paper develops a hybrid model for optimal order execution considering heterogeneous market makers and their inventory effects, capturing empirical price impact behaviors and providing a semi-explicit solution via stochastic control.

Contribution

It introduces a reduced form, scalable model for market impact that accounts for heterogeneity and derives a semi-explicit optimal trading strategy through stochastic control.

Findings

Model reproduces empirical power law price impact behavior.

Optimal strategies significantly reduce higher order moment risk.

Numerical results demonstrate improved execution performance.

Abstract

In this paper we explore optimal liquidation in a market populated by a number of heterogeneous market makers that have limited inventory-carrying and risk-bearing capacity. We derive a reduced form model for the dynamic of their aggregated inventory considering a proper scaling limit. The resulting price impact profile is shown to depend on the characteristics and relative importance of their inventories. The model is flexible enough to reproduce the empirically documented power law behavior of the price impact function. For any choice of the market makers characteristics, optimal execution within this modeling approach can be recast as a linear-quadratic stochastic control problem in which the value function and the associated optimal trading rate can be obtained semi-explicitly subject to solving a differential matrix Riccati equation. Numerical simulations are conducted to illustrate the performance of the resulting optimal liquidation strategy in relation to standard benchmarks. Remarkably, they show that the increase in performance is determined by a substantial reduction of higher order moment risk.