Asymptotic Pricing of Commodity Derivatives using Stochastic Volatility Spot Models

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Abstract
It is well known that stochastic volatility is an essential feature of commodity spot prices. By using methods of singular perturbation theory, we obtain approximate but explicit closed‐form pricing equations for forward contracts and options on single‐ and two‐name forward prices. The expansion methodology is based on a fast mean‐reverting stochastic volatility driving factor and leads to pricing results in terms of constant volatility prices, their Deltas and their Delta‐Gammas. Both the standard single‐factor mean‐reverting spot model and a two‐factor generalization, in which the long‐run mean is itself mean‐reverting, are extended to include stochastic volatility and each is analysed in detail. The stochastic volatility corrections can be used to efficiently calibrate option prices and compute sensitivities.

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