Commodity Derivatives Valuation with Autoregressive and Moving Average Components in the Price Dynamics

Abstract

In this paper we develop a continuous time factor model of commodity prices that allows for higher order autoregression and moving average components. The need for these components is documented by analyzing the convenience yield's time series dynamics. Making use of the affine model structure, closed-form pricing formulas for futures and options are derived. Empirically, a parsimonious version of the general model is estimated for the crude oil futures market. We demonstrate the model's superior performance in pricing nearby futures contracts in- and out-of sample. Most notably, the model substantially improves the pricing of long horizon contracts with information from the short end of the futures curve.

Keywords: Commodity Pricing, CARMA, Futures, Crude Oil

JEL Classification: G13, C50, Q40