Article Contents
Article Contents

# Pairs trading: An optimal selling rule

• Pairs trading involves two cointegrated securities. When divergence is underway, i.e., one stock moves up while the other moves down, a pairs trade is entered consisting of a short position in the outperforming stock and a long position in the underperforming one. Such a strategy bets the spread'' between the two would eventually converge. This paper is concerned with an optimal pairs-trade selling rule. In this paper, a difference of the pair is governed by a mean-reverting model. The trade will be closed whenever the difference reaches a target level or a cutloss limit. Given a fixed cutloss level, the objective is to determine the optimal target so as to maximize an overall return. This optimization problem is related to an optimal stopping problem as the cutloss level vanishes. Expected holding time and profit probability are also obtained. Numerical examples are reported to demonstrate the results.
Mathematics Subject Classification: Primary: 93E20, 91G80; Secondary: 49L20.

 Citation:

•  [1] C. Blanco and D. Soronow, Mean reverting processes - Energy price processes used for derivatives pricing and risk management, Commodities Now, (2001), 68-72. [2] A. Cowles and H. Jones, Some posteriori probabilities in stock market action, Econometrica, 5 (1937), 280-294.doi: 10.2307/1905515. [3] E. Fama and K. R. French, Permanent and temporary components of stock prices, Journal of Political Economy, 96 (1988), 246-273.doi: 10.1086/261535. [4] L. A. Gallagher and M. P. Taylor, Permanent and temporary components of stock prices: Evidence from assessing macroeconomic shocks, Southern Economic Journal, 69 (2002), 345-362.doi: 10.2307/1061676. [5] E. Gatev, W. N. Goetzmann and K. G. Rouwenhorst, Pairs trading: Performance of a relative-value arbitrage rule, Review of Financial Studies, Oxford University Press for Society for Financial Studies, 19 (2006), 797-827. [6] X. Guo and Q. Zhang, Optimal selling rules in a regime switching model, IEEE Transactions on Automatic Control, 50 (2005), 1450-1455.doi: 10.1109/TAC.2005.854657. [7] C. M. Hafner and H. Herwartz, Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis, Journal of Empirical Finance, 8 (2001), 1-34.doi: 10.1016/S0927-5398(00)00024-4. [8] J. Liu and A. Timmermann, Optimal convergence trade strategies, Review of Financial Studies, 26 (2013), 1048-1086.doi: 10.1093/rfs/hhs130. [9] G. Vidyamurthy, Pairs Trading: Quantitative Methods and Analysis, Wiley, Hoboken, NJ, 2004. [10] Q. Zhang, Stock trading: An optimal selling rule, SIAM J. Contr. Optim., 40 (2001), 64-87.doi: 10.1137/S0363012999356325. [11] H. Zhang and Q. Zhang, Trading a mean-reverting asset: Buy low and sell high, Automatica, 44 (2008), 1511-1518.doi: 10.1016/j.automatica.2007.11.003.