A study of commodity futures and futures options prices.

摘要

This study consists of three essays on pricing models of commodity futures and futures options. The first essay theoretically investigates how the price of commodity forward contracts, futures contracts and futures options are affected by stochastic convenience yields, stochastic interest rates and jumps in the spot price process. The assumption of stochastic convenience yields greatly affects futures and forward prices. The assumption of aIl arbitrage-free stochastic interest rate model affects futures prices but not forward prices. The assumption of jumps in the spot price process does not affect forward or futures prices but can greatly impact the pricing of options. In the second essay, the market prices of commodity futures options are used to imply the probability distribution of commodity futures prices. A four-parameter generalization of Black's model is used and all four parameters are implied from options prices. Significant degrees of skewness and kurtosis are found for the implied distribution of commodity futures prices. The third essay investigates the performance of a jump-diffusion model to price out-of-sample options. The jump-diffusion model performs considerably better than the geometric Brownian motion model of Black. Jump-Diffusion Asian option prices are also shown to differ considerably from geometric Brownian motion Asian option prices.