Empirical Pricing Performance in Long-Dated Crude Oil Derivatives: Do Models with Stochastic Interest Rates Matter?

Does modelling stochastic interest rates beyond stochastic volatility improve pricing performance on long-dated crude oil derivatives? To answer this question, we examine the empirical pricing performance of two forward price models for commodity futures and options: a deterministic interest rate - stochastic volatility model and a stochastic interest rate - stochastic volatility model. Both models allow for a correlation structure between the futures price process, the futures volatility process and the interest rate process. By estimating the model parameters from historical crude oil futures prices and option prices, we find that stochastic interest rate models improve pricing performance on long-dated crude oil derivatives, with the effect being more pronounced when the interest rate volatility is relatively high. Several results relevant to practitioners have also emerged from our empirical investigations. With regards to balancing the trade-off between precision and computational effort, we find that two-factor models would provide good fit on long-dated derivative prices thus there is no need to add more factors. We also find empirical evidence for a negative correlation between crude oil futures prices and interest rates.