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.