Lévy-Based Cross-Commodity Models and Derivative Valuation

Abstract

Energy commodities, such as oil, gas, and electricity, lack the liquidity of equity markets, have large costs associated with storage, exhibit high volatilities, and can have significant spikes in prices. Furthermore, and possibly more importantly, commodities tend to revert to long run equilibrium prices. Many complex commodity contingent claims exist in the markets, such as swing and interruptible options; however, the current method of valuation relies heavily on Monte Carlo simulations and tree-based methods. In this article, we develop a new cross-commodity modeling framework which accounts for jumps and cointegration in prices and introduce a new derivative valuation methodology by working in Fourier space. The method is based on the Fourier space time-stepping algorithm of Jackson, Jaimungal, and Surkov [J. Comput. Finance, 12 (2008), pp. 1–28] but is tailored for mean-reverting models. We demonstrate the utility of the method by applying it to European, American, and barrier options on a single commodity, to European and Bermudan spread options on two commodities, and to a particular class of swing options.