An Optimal Pairs-Trading Rule

TL;DR

This paper develops an optimal pairs trading strategy using a mean-reverting model for the spread, incorporating transaction costs and stop-loss limits, and characterizes the solution via HJB equations with numerical demonstrations.

Contribution

It introduces a novel optimal stopping framework for pairs trading with mean reversion, transaction costs, and stop-loss constraints, solved through quasi-variational inequalities.

Findings

Optimal trading boundaries are derived from quasi-algebraic equations.

The model accounts for fixed transaction costs and stop-loss limits.

Numerical examples illustrate the effectiveness of the proposed strategy.

Abstract

This paper is concerned with a pairs trading rule. The idea is to monitor two historically correlated securities. When divergence is underway, i.e., one stock moves up while the other moves down, a pairs trade is entered which consists of a pair to short the outperforming stock and to long the underperforming one. Such a strategy bets the "spread" between the two would eventually converge. In this paper, a difference of the pair is governed by a mean-reverting model. The objective is to trade the pair so as to maximize an overall return. A fixed commission cost is charged with each transaction. In addition, a stop-loss limit is imposed as a state constraint. The associated HJB equations (quasi-variational inequalities) are used to characterize the value functions. It is shown that the solution to the optimal stopping problem can be obtained by solving a number of quasi-algebraic equations. We provide a set of sufficient conditions in terms of a verification theorem. Numerical examples are reported to demonstrate the results.