Pricing Commodity Derivatives With Stochastic Term Structure Of Inthrest Rates And Convenience Yields

Commodity derivatives are becoming an increasingly important part of global derivatives market. A number of seminal papers have studied the problems about commodity derivatives, hedging and risk management. Based on previous studies, we develop a traceable and flexible ’unspanned stochastic volatility’ model of the term structure and study its applications for commodity derivatives prices.We first propose a short-term cost of carry model. In the model, the drift and quadratic variation of the short carry of cost are affine in three state variables (the short carry of cost, its long-term mean and variance) which follow a joint Markov process. Yet, futures prices are exponential affine functions of only two state variables (long-term mean of the carry of cost and variance), independent of the current carry of cost volatility level. Because this result holds for an arbitrary volatility process, such a process can be calibrated to match commodity derivatives prices. Furthermore, this model can be extended to fit any arbitrary term structure.On the basic of the previous short carry of cost model, we extend the short carry of cost process with two separate processes——the interest rate process and the convenience yield process. In particular, if the volatility process is specified to be affine(i.e.CIR process), using the technique of Fourier transform, a closed-form prices of European call options on futures contracts obtain. We propose the fractional Fourier transform algorithm(FRFT) which can be used to compute efficiently these prices.