Optimal liquidation for a risk averse investor in a one-sided limit order book driven by a Levy process

TL;DR

This paper develops an explicit model for optimal share liquidation in a one-sided limit order book driven by a Levy process, balancing market risk and execution costs for a risk-averse agent.

Contribution

It introduces a novel explicit solution for the optimal liquidation boundary in a Levy-driven market model with risk aversion.

Findings

Explicit optimal intervention boundary derived

Model captures realistic market risk via Levy process

Provides practical strategy for risk-averse liquidation

Abstract

In a one-sided limit order book, satisfying some realistic assumptions, where the unaffected price process follows a Levy process, we consider a market agent that wants to liquidate a large position of shares. We assume that the agent has constant absolute risk aversion and aims at maximising the expected utility of the cash position at the end of time. The agent is then faced with the problem of balancing the market risk and the cost of a rapid execution. In particular we are interested in how the agent should go about optimally submitting orders. Since liquidation normally takes place within a short period of time, modelling the risk as a Levy process should provide a realistic model with good statistical fit to observed market data, and thus the model should provide a realistic reflection of the agent's market risk. We reduce the optimisation problem to a deterministic two-dimensional singular problem, to which we are able to derive an explicit solution in terms of the model data. In particular we find an expression for the optimal intervention boundary, which completely characterise the optimal liquidation strategy.