Valuation of American commodity options

Abstract

In this dissertation, we present analytical option pricing formulas for European and American options in which the price dynamics of a risky asset follows a meanreverting process with time-dependent parameter. The process can be adapted to describe both nonseasonal and seasonal variation in price, especially, in commodity markets such as agricultural commodities. The formulas are derived based on the solutions of partial differential equations showing that the values of both European and American options can be decomposed into two parts: the payoff of the option at initial time and the time-integral over the lifetime of the option, which is driven by the time-dependent parameter, and in addition, by the optimal exercise boundary for the American option. Finally, numerical results and computational time obtained from the European option formula under various kinds of long-run mean functions have been compared with Monte Carlo simulations and Black-Scholestype formula obtained via probability approach. Moreover, examples of the option price behaviors under these time-dependent functions have been illustrated.