Pricing European commodity swaptions

In this paper, formulas for commodity swaptions are presented. By utilizing the forward price based approach a simple closed form solution for European swaptions is derived based on the assumption of deterministic volatility for lognormal variables. The formulas result from applying the Margrabe (1978) exchange option concept to the present problem. A special case of constant volatility yields the Black (1976) formula that has been the market standard in the interest rate swaption markets for many years.