Limit order trading with a mean reverting reference price

TL;DR

This paper analyzes optimal limit order strategies in a mean reverting asset price model, revealing that far from terminal, optimal prices become constant and focus on the mean, contrasting with models assuming Brownian motion.

Contribution

It extends existing limit order models by incorporating mean reversion, showing that optimal prices become static far from terminal and depend on market liquidity in intermediate regimes.

Findings

Optimal bid and ask prices are constant far from terminal in mean reverting models.

Limit orders tend to be executed regularly due to mean reversion.

Intermediate time regimes are influenced by market liquidity parameters.

Abstract

Optimal control models for limit order trading often assume that the underlying asset price is a Brownian motion since they deal with relatively short time scales. The resulting optimal bid and ask limit order prices tend to track the underlying price as one might expect. This is indeed the case with the model of Avellaneda and Stoikov (2008), which has been studied extensively. We consider here this model under the condition when the underlying price is mean reverting. Our main result is that when time is far from the terminal, the optimal price for bid and ask limit orders is constant, which means that it does not track the underlying price. Numerical simulations confirm this behavior. When the underlying price is mean reverting, then for times sufficiently far from terminal, it is more advantageous to focus on the mean price and ignore fluctuations around it. Mean reversion suggests that limit orders will be executed with some regularity, and this is why they are optimal. We also explore intermediate time regimes where limit order prices are influenced by the inventory of outstanding orders. The duration of this intermediate regime depends on the liquidity of the market as measured by specific parameters in the model.