Optimal Portfolio Liquidation with Limit Orders

TL;DR

This paper develops a unified model linking optimal portfolio liquidation scheduling with limit order pricing, addressing both execution and price risks simultaneously using stochastic control and backtesting in realistic scenarios.

Contribution

It introduces a novel approach that jointly optimizes trade scheduling and limit order prices, integrating market impact and execution risk into a single framework.

Findings

The model effectively balances execution and price risks.

Backtests demonstrate improved liquidation performance.

The approach outperforms traditional separate strategies.

Abstract

This paper addresses the optimal scheduling of the liquidation of a portfolio using a new angle. Instead of focusing only on the scheduling aspect like Almgren and Chriss, or only on the liquidity-consuming orders like Obizhaeva and Wang, we link the optimal trade-schedule to the price of the limit orders that have to be sent to the limit order book to optimally liquidate a portfolio. Most practitioners address these two issues separately: they compute an optimal trading curve and they then send orders to the markets to try to follow it. The results obtained here solve simultaneously the two problems. As in a previous paper that solved the "intra-day market making problem", the interactions of limit orders with the market are modeled via a Poisson process pegged to a diffusive "fair price" and a Hamilton-Jacobi-Bellman equation is used to solve the problem involving both non-execution risk and price risk. Backtests are carried out to exemplify the use of our results, both on long periods of time (for the entire liquidation process) and on slices of 5 minutes (to follow a given trading curve).