Model Uncertainty in Commodity Markets

Abstract

Agents who acknowledge that their models are incorrectly specified are said to be ambiguity averse, and this affects the prices they are willing to trade at. Models for prices of commodities attempt to capture three stylized features: seasonal trend, moderate deviations (a diffusive factor), and large deviations (a jump factor) both of which mean-revert to the seasonal trend. Here we model ambiguity by allowing the agent to consider a class of models absolutely continuous w.r.t. their reference model, but penalize candidate models that are far from it. We show that the buyer (seller) of a forward contract introduces a negative (positive) drift in the dynamics of the spot price, and enhances downward (upward) jumps so the prices they are willing to trade at are lower (higher) than that of the forward price under P. When ambiguity averse buyers and sellers employ the same reference measure they cannot trade because the seller requires more than what the buyer is willing to pay. Finally, we observe that when ambiguity averse agents price options written on the commodity forward, the effect of ambiguity aversion is strongest when the option is at-the-money, and weaker when it is deep in-the-money or deep out-of-the-money.

Keywords: Ambiguity aversion, Knightian uncertainty, Commodities, Certainty Equivalent, Robust Pricing, Indifference Pricing, Optimal Control