Markov Models for Commodity Futures: Theory and Practice
45 Pages Posted: 30 May 2008 Last revised: 30 Dec 2008
Date Written: September 30, 2008
This objective of this paper is to develop a generic, yet practical framework for construction of Markov models for commodity derivatives. We aim for sufficient richness to permit applications to a broad variety of commodity markets, including those that are characterized by seasonality and by spikes in the spot process. In the first, largely theoretical, part of the paper we derive a series of useful results about low-dimensional Markov representation of the dynamics of an entire term structure of futures prices. Extending previous results in the literature, we cover jump-diffusive models with stochastic volatility as well as several classes of regime-switch models. To demonstrate the process of building models for a specific commodity market, the second part of the paper applies a selection of our theoretical results to the exercise of constructing and calibrating derivatives trading models for USD natural gas. Special attention is paid to the incorporation of empirical seasonality effects in futures prices, in implied volatilities and their smile, and in correlations between futures contracts of different maturities. European option pricing in our proposed gas model is closed-form and of the same complexity as the Black-Scholes formula.
Keywords: commodity futures, natural gas, seasonality, jump-diffusion, stochastic volatility, regime-switching, Markov model
JEL Classification: G13, C63
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