Misspecification in term structure models of commodity prices: Implications for hedging price risk

Abstract

Stochastic dynamics of commodity prices and valuation of derivative contracts have long been studied in the field of financial economics. In the literature a common approach is to specify a stochastic dynamics of the underlying assets and derive from the suggested model valuation formulas of various derivative contracts whose payoff depends on the realization of the underlying asset value. Recently, models with additional latent factors and more flexible stochastic process of each factor have been suggested. Although these complex models tend to fit better to the observed data, it is often understated that this modeling approach only approximates the true stochastic process of the underlying asset values. This approximation bias can be substantial in magnitude for a storable commodity with significant demand and/or supply seasonality, for which equilibrium path of spot and futures prices cannot be expressed in reduced form, as shown by the theory of storage.This study examines conventional term-structure models of commodity prices. In particular, this study quantifies the approximation bias of these conventional models through comparing them with an alternative approach of modeling the variance of daily futures returns directly by flexible non-parametric functions so as to allow the model to replicate highly non-linear price dynamics of storable commodities. Empirical applications of the models reveal that, for all four commodities (gold, crude oil, natural gas, and corn) examined in this study, the volatility of daily futures prices is more complex than the pattern as implied by the dynamics stipulated in the conventional term-structure models. In particular, all four commodities exhibit a strong time-to-maturity effect as well as a significant seasonal pattern in both levels and compositions (among two factors and idiosyncratic errors) of volatility of daily futures returns. Conventional termstructure models draw incorrect portraits of volatility dynamics as well as incorrect correlation among concurrently traded contracts with different maturity dates, which lead these models to suggest hedging strategies that are considerably less effective than the strategy based on the model of futures returns.