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

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