Choice of copulas in explaining stock market contagion

Abstract

We provide in this paper an assessment of how well the Archimedean class of copulas can explain equity market contagion across regions. In particular we examine the Clayton, the Gumbel, and the Frank copulas. Three representative large equity markets across the globe in U.S., in U.K., and in Japan are studied. The S&P 500, FTSE 100, and the Nikkei 225 stock market indices of the three countries are used to compute proxy large portfolio returns. The joint daily return vectors of these three equity markets are tracked over the period from the beginning of January 1990 till end of April 2012. The Kullback-Leibler distances (divergences) or relative entropy of the copulas with respect to the empirical distribution are compared with a benchmark t-copula relative entropy. We then narrow the focus on the conditional joint tail losses of the multivariate return distribution using the Pareto Type II distribution to model the tails. The maximum likelihood approach is used for estimating the parameters of the marginal conditional tail distributions and the copulas. The observed joint returns in the loss region of at least one standard deviation away from the mean are then matched in frequencies across 27 three by three cells with the theoretical probabilities based on the estimated parameters under the competing copulas. A goodness-of-fit test together with the relative entropy results show that the Clayton copula is statistically the most appropriate copula in explaining contagion during this sampling period. © 2013 Springer-Verlag Berlin Heidelberg.