  We introduce a multi-factor stochastic volatility model based on the
CIR/Heston volatility process that incorporates seasonality and the Samuelson
effect. First, we give conditions on the seasonal term under which the
corresponding volatility factor is well-defined. These conditions appear to be
rather mild. Second, we calculate the joint characteristic function of two
futures prices for different maturities in the proposed model. This
characteristic function is analytic. Finally, we provide numerical
illustrations in terms of implied volatility and correlation produced by the
proposed model with five different specifications of the seasonality pattern.
The model is found to be able to produce volatility smiles at the same time as
a volatility term-structure that exhibits the Samuelson effect with a seasonal
component. Correlation, instantaneous or implied from calendar spread option
prices via a Gaussian copula, is also found to be seasonal.
