|M.Sc Student||Dourban Alon|
|Subject||Threshold Policy for Purchasing Assets with a Mean Reverting|
|Department||Department of Industrial Engineering and Management||Supervisor||Dr. Liron Yedidsion|
|Full Thesis text|
Commodities are one of the most traded sectors in the financial world. As the price of commodities tends to fluctuate strongly, the optimal purchasing point should be examined carefully. Our work offers an original method for optimizing purchasing decisions within a given time horizon for commodities whose price follows the mean reverting Ornstein-Uhlenbeck (O-U) process. The optimal policy is based on a simple threshold function that indicates whether to purchase the commodity if its price is below the threshold. We prove that the threshold policy is optimal, and construct its basic characteristics. Then, we develop the method for calculating the threshold policy, which is obtained by representing the expected value of the optimal purchasing price in a recursive form. The recursive function integrates two general functions: the probability that the price will fall below the threshold; and the expectation of the price conditioned on this event. These functions are closed form functions. The threshold is found using a bisection search method of these functions' value. We show that with minor modifications our method can be used to price a mean-reverting American option. As far as we know, there is no closed form technique for pricing such options in the literature. We finish a numerical example that illustrates the threshold calculation.