A comparison study of copula models for European Financial Index Returns

Abstract

In this paper, we introduce a new approach to modeling dependence between international financial returns over time, combining time-varying copulas and the Markov switching model. We apply these copula models and also those proposedby Patton (2006), Jondeau and Rockinger (2006) and Silva Filho, Ziegelmann,and Dueker (2012) to the return data of the FTSE-100, CAC-40 and DAX indexes. We are particularly interested in comparing these methodologies in terms of the resulting dynamics ofdependence and the models’abilities to forecast possible capital losses. Because risks related to extreme events are important for risk management, we compare and select the models based on VaR forecasts. Interestingly, all the models identify a long period of high dependence between the returns beginning in 2007, when the subprime crisis was evolving. Surprisingly, the elliptical copulas perform best in forecasting the extreme quantiles of the portfolios returns.