An Optimal Execution Problem with a Geometric Ornstein-Uhlenbeck Price Process

TL;DR

This paper investigates an optimal execution strategy when security prices follow a mean-reverting geometric Ornstein-Uhlenbeck process, revealing that a mixed approach of block and gradual liquidation is optimal, influenced by market impact and price recovery.

Contribution

It introduces a novel optimal execution model with a geometric Ornstein-Uhlenbeck process, highlighting the importance of price recovery and impact transience in strategy formulation.

Findings

Optimal strategy combines block and gradual liquidation.

Mean-reversion influences the form of the optimal strategy.

Price recovery and impact transience are key to gradual liquidation.

Abstract

We study an optimal execution problem in the presence of market impact where the security price follows a geometric Ornstein-Uhlenbeck process, which implies the mean-reverting property, and show that the optimal strategy is a mixture of initial/terminal block liquidation and gradual intermediate liquidation. The mean-reverting property describes a price recovery effect that is strongly related to the resilience of market impact, as described in several papers that have studied optimal execution in a limit order book (LOB) model. It is interesting that despite the fact that the model in this paper is different from the LOB model, the form of our optimal strategy is quite similar to those obtained for an LOB model. Moreover, we discuss what properties cause gradual liquidation as an optimal strategy by studying various cases and find out that not only "convexity of market impact function" but also "price recovery effect" (or, in other words, transience of market impact) are essential to make a trader execute the security gradually to mitigate the effect of market impact.