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

Phong Luu, Jingzhi Tie and Qing Zhang
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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

Risks, 2018, vol. 6, issue 4, 1-15

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.

Keywords: mean reversion; HJB equation; quasi-variational inequalities; smooth-fit method (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2018
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