Non-Affine Stochastic Volatility With Seasonal Trends

We propose a new stochastic volatility model for pricing options on assets that exhibit seasonal trends in volatility. Such assets are prevalent among commodities, with futures on grains and energy being an example. The model is based on the 3/2 stochastic volatility model, but includes a cyclical long-run volatility component. The model yields a closed-form characteristic function which can be used to rapidly calibrate the model to benchmark options. We test the model on market data and show that the model proposed here allows for significantly better empirical fit to option prices on corn and wheat futures than the unmodified 3/2 model.