Copula-Based Dependence Analysis of U.S. Stock Index and Futures Time Series in Financial Crisis

Abstract

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. In this study, we discussed the choice of an appropriate copula function aimed at adequately capturing the dependence between the return time series of S&P 500 stock index and futures in U.S. financial crisis. By comparing with the Gaussian, Student’s t, Gumbel, Clayton and Frank copula, we concluded that Gumbel copula function can provide a better fit to the empirical data, and therefore well extract the dependence structure between S&P 500 stock index and futures in financial crisis.

Key words: Stock index; Dependence; Copula; Financial crisis