A Flexible Commodity Skew Model with Maturity Effects

Abstract: We propose a non-parametric extension with leverage functions to the Andersen commodity curve model. We calibrate this model to market data for WTI and NG including option skew at the standard maturities. While the model can be calibrated by an analytical formula for the deterministic rate case, the stochastic rate case demands estimation of an expectation for which we employ Monte Carlo simulation. We find that the market smile is captured for the deterministic rate case; and with relatively low number of paths, for the stochastic rate case. Since there is typically at most one standard maturity with liquid volatility data for each futures contract, there is flexibility on the shape of nonstandard maturity implied volatility and how the total implied variance accumulates. We equip the model with different total implied variance accumulators to demonstrate that flexibility.