  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.
