Approximately optimal trade execution strategies under fast mean-reversion

TL;DR

This paper develops a model for optimal trade execution under uncertain, fast mean-reverting market conditions, incorporating high-frequency data to estimate parameters and assess strategies amid microstructure noise.

Contribution

It introduces a novel framework modeling uncertain liquidity and volatility with fast mean-reversion, applying singular perturbation methods for optimal execution strategies.

Findings

Derived approximate optimal strategies using singular perturbation techniques.

Provided estimation methods for model parameters from high-frequency data.

Numerically validated strategies considering microstructure noise effects.

Abstract

In a fixed time horizon, appropriately executing a large amount of a particular asset -- meaning a considerable portion of the volume traded within this frame -- is challenging. Especially for illiquid or even highly liquid but also highly volatile ones, the role of "market quality" is quite relevant in properly designing execution strategies. Here, we model it by considering uncertain volatility and liquidity; hence, moments of high or low price impact and risk vary randomly throughout the trading period. We work under the central assumption: although there are these uncertain variations, we assume they occur in a fast mean-reverting fashion. We thus employ singular perturbation arguments to study approximations to the optimal strategies in this framework. By using high-frequency data, we provide estimation methods for our model in face of microstructure noise, as well as numerically assess all of our results.