A contango-constrained model for storable commodity prices

Abstract

In this article we develop a model for the commodity price dynamics under the risk-neutral measure where the spot price switches between two distinct stochastic processes depending on whether or not inventory is being held. Speciflcally, whenever the drift of the spot price exceeds the cost of carrying inventory (interest rate plus storage costs) the inventory is being held. Conversely, whenever the drift of the spot price is less than the cost of carry, all the inventory is sold and the storage facility becomes empty. If inventory is being held, we assume that the spot price follows a geometric Brownian motion with drift equal to the cost of carrying inventory. Otherwise, the price follows a Ornstein-Uhlenbeck stochastic process. This model verifles arbitrage-free arguments since the commodity price process has a drift lees or equal to the cost of carry under the risk neutral measure. We illustrate and analyze the properties of the spot price and the forward curves implied by this model using numerical examples. The spot price sample paths and the corresponding forward curves are constructed by applying trinomial tree techniques. For comparison, we also provide the equivalent numerical examples for the single-factor model provided by Schwartz (1997), which correspond to the unconstrained version of the spot price process in this model.