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A Threshold Type Policy for Trading a Mean-Reverting Asset with Fixed Transaction Costs

Author

Listed:
  • Phong Luu

    (Department of Mathematics, University of North Georgia, Oakwood, GA 30566, USA)

  • Jingzhi Tie

    (Department of Mathematics, University of Georgia; Athens, GA 30602, USA)

  • Qing Zhang

    (Department of Mathematics, University of Georgia; Athens, GA 30602, USA)

Abstract

A mean-reverting model is often used to capture asset price movements fluctuating around its equilibrium. A common strategy trading such mean-reverting asset is to buy low and sell high. However, determining these key levels in practice is extremely challenging. In this paper, we study the optimal trading of such mean-reverting asset with a fixed transaction (commission and slippage) cost. In particular, we focus on a threshold type policy and develop a method that is easy to implement in practice. We formulate the optimal trading problem in terms of a sequence of optimal stopping times. We follow a dynamic programming approach and obtain the value functions by solving the associated HJB equations. The optimal threshold levels can be found by solving a set of quasi-algebraic equations. In addition, a verification theorem is provided together with sufficient conditions. Finally, a numerical example is given to illustrate our results. We note that a complete treatment of this problem was done recently by Leung and associates. Nevertheless, our work was done independently and focuses more on developing necessary optimality conditions.

Suggested Citation

  • Phong Luu & Jingzhi Tie & Qing Zhang, 2018. "A Threshold Type Policy for Trading a Mean-Reverting Asset with Fixed Transaction Costs," Risks, MDPI, vol. 6(4), pages 1-15, September.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:4:p:107-:d:172739
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    References listed on IDEAS

    as
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    3. Tim Leung & Xin Li & Zheng Wang, 2015. "Optimal Multiple Trading Times Under the Exponential OU Model with Transaction Costs," Papers 1504.04682, arXiv.org.
    4. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    5. 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.
    6. Stefano Baccarin & Daniele Marazzina, 2014. "Optimal impulse control of a portfolio with a fixed transaction cost," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(2), pages 355-372, June.
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