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An Optimal Pairs-Trading Rule

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  • Qingshuo Song
  • Qing Zhang
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    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.

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    File URL: http://arxiv.org/pdf/1302.6120
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1302.6120.

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    Date of creation: Feb 2013
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    Handle: RePEc:arx:papers:1302.6120

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    Web page: http://arxiv.org/

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    1. Liam A. Gallagher & Mark P. Taylor, 2002. "Permanent and Temporary Components of Stock Prices: Evidence from Assessing Macroeconomic Shocks," Southern Economic Journal, Southern Economic Association, vol. 69(2), pages 345-362, October.
    2. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 96(2), pages 246-73, April.
    3. Hafner, Christian M. & Herwartz, Helmut, 2001. "Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis," Journal of Empirical Finance, Elsevier, Elsevier, vol. 8(1), pages 1-34, March.
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