Abstract
We introduce a multi-factor stochastic volatility model with expiry dependent damping factors. This futures-based model is able to capture the Samuelson effect and the volatility smile displayed by commodity futures and option contracts. We calculate the joint characteristic function of two futures contracts in the model in analytic form and use it to price calendar spread options. We then propose analytical expressions to obtain the copula and copula density directly from the joint characteristic function of a pair of futures. In an empirical application we perform a joint calibration to market prices of vanilla and calendar spread options on WTI. We provide evidence that the model is able to produce the desired stylized facts in terms of implied volatility and at the same time to fit market prices of calendar spread options. In particular, we observe a phenomenon we call the Samuelson correlation effect.
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