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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
    1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    2. Liam A. Gallagher & Mark P. Taylor, 2002. "Permanent and Temporary Components of Stock Prices: Evidence from Assessing Macroeconomic Shocks," Southern Economic Journal, John Wiley & Sons, vol. 69(2), pages 345-362, October.
    3. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    4. 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.
    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. Liam A. Gallagher & Mark P. Taylor, 2002. "Permanent and Temporary Components of Stock Prices: Evidence from Assessing Macroeconomic Shocks," Southern Economic Journal, John Wiley & Sons, vol. 69(2), pages 345-362, October.
    7. Tim Leung & Xin Li & Zheng Wang, 2015. "Optimal Multiple Trading Times Under the Exponential OU Model with Transaction Costs," Papers 1504.04682, arXiv.org.
    8. 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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