Jumps in Commodity Prices: New Approaches for Pricing Plain Vanilla Options

Abstract

We present a new term-structure model for commodity futures prices based on Trolle and Schwartz (2009) which we extend by incorporating multiple jump processes. Our work explores the valuation of plain vanilla options on futures prices when the spot price follows a log-normal process, the forward cost of carry curve and the volatility are stochastic variables, and the spot price and the forward cost of carry allow for time-dampening jumps. We obtain an analytical representation of the characteristic function of the futures prices and, hence, also for plain vanilla option prices using the fast Fourier transform (FFT) methodology. We price options on WTI crude oil futures contracts using our model and extant models. We obtain higher accuracy than earlier models and save significantly in computing time.

Keywords: Commodities, crude oil, futures prices, option pricing, Fourier transform, fast Fourier transform, term-structure model, analytical solution, stochastic volatility, jump-diffusion.

JEL Classification: G13