Dependence Structure and Hedging of U.S. Spot and Futures Markets in Financial Crisis

Abstract

The main objective of this study is to measure appropriately the dependence structure and optimal hedge ratio of U.S. spot and futures markets in financial crisis. In much empirical literature it has been demonstrated that linear Pearson correlation is not an appropriate dependence measure for non-normal distributions. This inadequacy of correlation requires an appropriate dependence measure: the copula. Copula modeling has become an increasingly popular tool in finance to model assets returns dependency as it can overcome the limitations of correlation when extreme losses occurred. The contribution of this paper is in two aspects. First, an appropriate copula function is discovered to capture the dependence structure of S&P 500 spot and futures in financial crisis adequately. Second, Gumbel copula function is exploited, with threshold GARCH model as marginals, to construct a Gumbel copula-threshold-GARCH model to estimate the optimal hedge ratio, simultaneously capturing asymmetric nonlinear behaviour in univariate returns of spot and futures markets and bivariate dependency.