Optimal Pairs Trading Rules

Abstract

This thesis derives an optimal trading rule for a pair of historically correlated stocks. When one stock's price increases and the other one's decreases, a trade of the pair is triggered. The idea is to short the winner and to long the loser with the hope that the prices of the two assets will converge again. In this thesis the spread of the two stocks is governed by a mean-reverting model. The objective is to trade the pair in such a way as to maximize an overall return. The same slippage cost is imposed on every trade. Furthermore, a local-time process to the spread is introduced in order to avoid infinitely large gains. We use the associated Hamilton-Jacobi-Bellman equations to characterize the value functions which are solved by using the smooth-fit method. It is shown that the solution of the optimal pairs trading problem can be obtained by solving a set of nonlinear equations. Additionally, a set of sufficient conditions is provided in form of a verification theorem. The thesis concludes with a numerical example.