Closed-form analytical solutions for options on agricultural futures with seasonality and stochastic convenience yield

Stochastic commodity price models play a significant role in the pricing and hedging of commodity derivatives and real assets. This paper proposes a commodity pricing model that extends the Ewald and Ouyang two-factor model by adding a time-varying function into the volatility term of convenience yield process to describe seasonality. The stochastic factors in the model are the spot price of the commodity is assumed to follow geometrical Brownian motion process with a stochastic drift, the instantaneous convenience yield follows a mean-reverting Ornstein-Uhlenbeck stochastic process with time-varying seasonal volatility. The model we propose is analytically tractable and allows us to derive closed-form pricing formulas for futures and options by using the Mellin transform method. In addition, we provide the experiments results to illustrate the important properties of commodity futures options with numerical table and graphs.