Valuation of Commodity Futures and Options under Stochastic Convenience Yields, Interest Rates, and Jump Diffusions in the Spot

This paper investigates the effects of stochastic convenience yields, stochastic interest rates, and jumps in the spot price on the pricing of commodity futures, forwards, and futures options. Numerical examples show that one-factor prices differ materially from the stochastic convenience yield two-factor prices when convenience yield is considerably above its long-term average. The extension to a three-factor model with stochastic interest rates leads to a different futures price but the forward price is unchanged. The extension of the three-factor model to include jumps in the spot price process does not affect forward or futures prices but it can have an impact on options prices. The model is applied to price the present value of future cash flows from a real asset.