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.
Highlights
This paper is about trading a mean-reverting asset
It is common in financial markets to use a mean-reversion model to capture price movements having the tendency to move towards an “equilibrium”
Note that all the threshold levels x0, x1, and x2 are below the equilibrium b = 2
Summary
This paper is about trading a mean-reverting asset. A common strategy in mean reversion trading is to buy low and sell high. Trading under mean reversion models was considered by (Zhang and Zhang 2008) They obtained a threshold type strategy and were able to characterize these two key (low and high) levels in terms of the mean reversion parameters. This issue was successfully addressed in a recent work (Leung et al 2015) They studied an optimal multiple trading under a mean reversion model with fixed transaction costs. They solved a double stopping problem following a probabilistic approach. The problem is formulated based on a mean reversion model, relevant properties of the value functions are established, the associated HJB equations and their solutions are obtained, and a verification theorem is provided that guarantees the optimality of our trading policy.
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