Optimal Trade Execution in Illiquid Markets

TL;DR

This paper analyzes optimal trade execution strategies in illiquid markets with discrete order flow, considering various stochastic models for order arrivals, and provides computational methods and comparisons for these models.

Contribution

It introduces a comprehensive analysis of optimal execution strategies under different Poisson-based order flow models, including regime-switching and hidden Markov models.

Findings

Optimal strategies depend on the order flow model.

Regime-switching models capture market state changes.

Computational examples illustrate strategy differences.

Abstract

We study optimal trade execution strategies in financial markets with discrete order flow. The agent has a finite liquidation horizon and must minimize price impact given a random number of incoming trade counterparties. Assuming that the order flow $N$ is given by a Poisson process, we give a full analysis of the properties and computation of the optimal dynamic execution strategy. Extensions, whereby (a) $N$ is a fully-observed regime-switching Poisson process; and (b) $N$ is a Markov-modulated compound Poisson process driven by a hidden Markov chain, are also considered. We derive and compare the properties of the three cases and illustrate our results with computational examples.