This guide introduces Miltersen & Schwartz commodity options, and provides a pricing spreadsheet.
Pricing commodities is often difficult because the various influencing parameters are not known, either at all or to a high degree of certainty. For example, the spot price is often difficult to obtain (often being indirectly calculated from a futures contract near to maturity), and the instantaneous yield is often estimated. Hence pricing models based on future contracts are often used.
The Miltersen & Schartz (1998) model is a closed-form three-factor model for pricing commodity options. It is based on a generalization of the Black-Scholes equation, and its characteristics include log-normally distributed returns and risk-free rates, stochastic convenience yields and interest rates.
The lag between the time to maturity and the time to maturity of the futures price has a considerable effect on the option price.