Dynamic Cross-Hedge Ratios: An Application of Copula Models

In this study, we propose a new approach to estimating optimal dynamic cross-hedge ratios. In particular, we apply copula models to discuss the use of corn futures contracts to cross hedge grain sorghum, and the use of Kansas wheat futures contracts to cross hedge barley. Hedge (or cross-hedge) ratios are generally estimated by using the variances of cash and futures returns and the correlation between these returns. We compute the time-varying variances of cash and futures returns by applying the Error Correction Model (ECM) with GARCH error terms. The time-varying correlation term in the dynamic cross-hedge ratio is obtained from eight copula models – two elliptical copulas (Gaussian and Student’s-t) and six Archimedean copulas (Clayton, rotated Clayton, Gumbel, rotated Gumbel, Frank, and Plackett). We use maximum likelihood estimation techniques to estimate the copula models and compare the performance of these copula models by their maximum likelihood values. Results confirm the significant linkages between these markets and demonstrate the effectiveness of cross-hedging as a mechanism for managing price risks.