Pricing option on commodity futures under string shock

Abstract

Forward curve movements, particularly of industrial and energy commodities, suggests that futures price do not move in tandem with the spot price, and not all futures contracts move in the same direction. We incorporate these subtleties into our model with parsimony. This article offers a new approach to value commodity derivatives by using string shock. We use it to perturb the term structure of future convenience yield as if every futures contract has its source of risk. The no-arbitrage condition on the drift of future convenience yield and closed-form formula for the European call option written on a futures contract is derived. Our model has separate volatility and correlation functions that ensure easier parameterization and calibration to market data. We compare absolute and relative option pricing errors of our model with the two factor Schwartz (1997) model for 440 trading days. It is found that the new string shock based model has better performance than the Schwarz’s model regarding having lesser pricing errors.