We construct a novel class of pure jump and jump-diffusion commodity models with state dependent mean-reverting jumps and stochastic volatility by applying time changes to the classical commodity models based on mean-reverting diffusions. The initial futures curve is an input into the model, and the dynamics of the futures curves over time exhibits mean-reverting jumps and stochastic volatility. Time inhomogeneous behavior such as seasonality can also be modeled by applying a deterministic time change. We obtain analytical solutions for the pricing of commodity options on futures through the spectral expansion methodology. The models are flexible enough to capture a variety of implied volatility smile patterns observed in energy, metals, and agricultural commodities futures options. This is joint work with Vadim Linetsky.
Speaker: Lingfei Li, Northwestern University