Multi-Factor Levy Processes and Regime Switching for Commodities

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 talk, I will describe a new model of cointegrated prices containing mean-reverting jumps and diffusions as well as a new valuation framework 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. I will demonstrate the utility of the method by applying it to the valuation of European, American, Spread and swing options. In addition, I will discuss the real option to invest in an oil field where the volume is stochastic but is discovered as time evolves.

[ This is based on joint work with Vladimir Surkov, Ph.D. candidate, Dept. Computer Science, U. Toronto]