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Optimal closing of a pair trade with a model containing jumps

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  • Stig Larsson
  • Carl Lindberg
  • Marcus Warfheimer

Abstract

A pair trade is a portfolio consisting of a long position in one asset and a short position in another, and it is a widely applied investment strategy in the financial industry. Recently, Ekstr\"om, Lindberg and Tysk studied the problem of optimally closing a pair trading strategy when the difference of the two assets is modelled by an Ornstein-Uhlenbeck process. In this paper we study the same problem, but the model is generalized to also include jumps. More precisely we assume that the above difference is an Ornstein-Uhlenbeck type process, driven by a L\'evy process of finite activity. We prove a verification theorem and analyze a numerical method for the associated free boundary problem. We prove rigorous error estimates, which are used to draw some conclusions from numerical simulations.

Suggested Citation

  • Stig Larsson & Carl Lindberg & Marcus Warfheimer, 2010. "Optimal closing of a pair trade with a model containing jumps," Papers 1004.2947, arXiv.org.
  • Handle: RePEc:arx:papers:1004.2947
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    References listed on IDEAS

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    3. John F. Geweke, 1991. "Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments," Staff Report 148, Federal Reserve Bank of Minneapolis.
    4. Paulo J. R. Pinheiro & João Manuel Andrade e Silva & Maria de Lourdes Centeno, 2003. "Bootstrap Methodology in Claim Reserving," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(4), pages 701-714.
    5. Gisler, Alois & Wüthrich, Mario V., 2008. "Credibility for the Chain Ladder Reserving Method," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 38(02), pages 565-600, November.
    6. England, P.D. & Verrall, R.J., 2002. "Stochastic Claims Reserving in General Insurance," British Actuarial Journal, Cambridge University Press, vol. 8(03), pages 443-518, August.
    7. England, Peter & Verrall, Richard, 1999. "Analytic and bootstrap estimates of prediction errors in claims reserving," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 281-293, December.
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