Mathematical Control and Related Fields (MCRF)

Pairs trading: An optimal selling rule

Pages: 489 - 499, Volume 5, Issue 3, September 2015      doi:10.3934/mcrf.2015.5.489

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Kevin Kuo - Citi, 2859 Paces Ferry Rd., Ste. 900, Atlanta, GA 30339, United States (email)
Phong Luu - Department of Mathematics, University of Georgia, Athens, GA 30602, United States (email)
Duy Nguyen - Department of Mathematics, Massachusetts College of Liberal Arts, 375 Church Street, North Adams, MA 01247, United States (email)
Eric Perkerson - Department of Mathematics, University of Georgia, Athens, GA 30602, United States (email)
Katherine Thompson - Department of Mathematics, University of Georgia, Athens, GA 30602, United States (email)
Qing Zhang - Department of Mathematics, University of Georgia, Athens, GA 30602, United States (email)

Abstract: 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.

Keywords:  Pairs trading, optimal selling, mean-reverting process.
Mathematics Subject Classification:  Primary: 93E20, 91G80; Secondary: 49L20.

Received: March 2014;      Revised: June 2014;      Available Online: July 2015.

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