Optimal Mean-Reverting Spread Trading: Nonlinear Integral Equation Approach

TL;DR

This paper develops a nonlinear integral equation approach to solve optimal stopping problems for mean-reverting spread trading strategies modeled by the Ornstein-Uhlenbeck process, providing a numerical method to determine optimal trading boundaries.

Contribution

It introduces a novel nonlinear integral equation framework for solving optimal double stopping problems in mean-reverting spread trading, extending previous methods.

Findings

Derivation of Volterra-type integral equations for optimal boundaries

Numerical computation of optimal trading strategies

Application to multiple trading strategies including long-short and chooser

Abstract

We study several optimal stopping problems that arise from trading a mean-reverting price spread over a finite horizon. Modeling the spread by the Ornstein-Uhlenbeck process, we analyze three different trading strategies: (i) the long-short strategy; (ii) the short-long strategy, and (iii) the chooser strategy, i.e. the trader can enter into the spread by taking either long or short position. In each of these cases, we solve an optimal double stopping problem to determine the optimal timing for starting and subsequently closing the position. We utilize the local time-space calculus of Peskir (2005a) and derive the nonlinear integral equations of Volterra-type that uniquely char- acterize the boundaries associated with the optimal timing decisions in all three problems. These integral equations are used to numerically compute the optimal boundaries.