The Shape of the Optimal Hedge Ratio: Modeling Joint Spot-Futures Prices using an Empirical Copula-GARCH Model

Commodity cash and futures prices have been rising steadily since 2006. As evidenced by the April 2008 Commodity Futures Trading Commission Agricultural Forum, there is much concern among traditional futures and options market participants that the usefulness of commodity derivatives has been compromised. When basis risk is particularly high, dynamic hedging methods may be helpful despite their complexity and higher transaction costs. To assess the potential benefits of dynamic hedging in volatile times, this paper proposes a novel, empirical copula-based method to estimate GARCH models and to compute time-varying hedge ratios. This approach allows a nonlinear, asymmetric dependence structure between cash and futures prices. The paper addresses four principal questions: (1) Does the empirical copula-GARCH method overcome traditional limitations of dynamic hedging methods? (2) How does the empirical copula- GARCH hedging approach perform, for storable agricultural commodities, compared with traditional GARCH and Minimum Variance (static) hedging methods? (3) Is dynamic hedging more or less effective in the post-2006 biofuels expansion time period? (4) How sensitive is the ranking of methods to the hedging effectiveness criterion used? Preliminary findings suggest that the empirical copula-GARCH approach leads to superior hedging effectiveness based on some, but not all, risk criteria.