A Levy Based Framework for Commodity Derivative Valuation via FFT

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 most 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 framework for dealing with mean-reverting jump-diffusion (and pure jump) models by working in Fourier space. The method is based on the Fourier space time stepping algorithm of Jackson, Jaimungal, and Surkov (2008), but is tailored for mean-reverting models. We demonstrate the utility of the method by applying it to the valuation of European, American and barrier options on a single underlier, European and Bermudan spread options on two-dimensional underliers, and swing options.

Keywords: Multi asset commodity derivatives, Option pricing, Mean reverting Levy processes, Fourier transform based method

JEL Classifications: G12, G13, C63

Working Paper Series