A flexible commodity skew model with maturity effects

Orcan Ögetbil and Bernhard Hientzsch

Abstract

We propose a nonparametric extension with leverage functions to the Andersen commodity curve model. We calibrate this model to market data for West Texas Intermediate crude oil and for natural gas, including option skew at the standard maturities. Since there is typically one standard maturity with liquid volatility data for most futures contracts, there is flexibility around the shape of nonstandard maturity implied volatility and how the total implied variance (TIV) accumulates. We equip the model with different TIV accumulators to exhibit that flexibility. In the deterministic rate case the model can be calibrated by an analytical formula, whereas the stochastic rate case demands the 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 a relatively low number of paths, for the stochastic rate case. We demonstrate the calibrated model for pricing Asian options and estimating the expected positive and negative exposures for a commodity swap under several TIV accumulation schemes.