IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1302.6120.html
   My bibliography  Save this paper

An Optimal Pairs-Trading Rule

Author

Listed:
  • Qingshuo Song
  • Qing Zhang

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.

Suggested Citation

  • Qingshuo Song & Qing Zhang, 2013. "An Optimal Pairs-Trading Rule," Papers 1302.6120, arXiv.org.
  • Handle: RePEc:arx:papers:1302.6120
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1302.6120
    File Function: Latest version
    Download Restriction: no

    References listed on IDEAS

    as
    1. Hafner, Christian M. & Herwartz, Helmut, 2001. "Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis," Journal of Empirical Finance, Elsevier, vol. 8(1), pages 1-34, March.
    2. 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.
    3. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-273, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Krauss, Christopher, 2015. "Statistical arbitrage pairs trading strategies: Review and outlook," FAU Discussion Papers in Economics 09/2015, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    2. Minh Man Ngo & Huyen Pham, 2014. "Optimal switching for pairs trading rule: a viscosity solutions approach," Papers 1412.7649, arXiv.org.
    3. Tim Leung & Yerkin Kitapbayev, 2017. "Optimal Mean-Reverting Spread Trading: Nonlinear Integral Equation Approach," Papers 1701.00875, arXiv.org, revised Jan 2017.
    4. repec:kap:annfin:v:13:y:2017:i:2:d:10.1007_s10436-017-0295-y is not listed on IDEAS

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1302.6120. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators). General contact details of provider: http://arxiv.org/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.