Abstract
This article is concerned with the study of the tail correlation among equity indices by means of dynamic copula functions. The main idea is to consider the impact of the use of copula functions in the accuracy of the model’s parameters and in the computation of Value-at-Risk (VaR). Results show that copulas provide more sophisticated results in terms of the accuracy of the forecasted VaR, in particular, if they are compared with the results obtained from Dynamic Conditional Correlation (DCC) model.
Highlights
One common mistake in portfolio theory is to assume that multivariate financial returns are normally distributed
The null hypothesis of a BB1–generalized autoregressive score (GAS) copula is rejected at all significance levels for both FTSE–DAX and FTSE-IBEX indices
P-values for the Symmetrized Joe-Clayton (SJC)–GAS copula are significant at 10% level in the case of the FTSE–IBEX and only at 1% level in the case of the FTSE–DAX
Summary
One common mistake in portfolio theory is to assume that multivariate financial returns are normally distributed. In a further work, Oh and Patton (2018) improved the time-varying equation for copulas via the so-called generalized autoregressive score (GAS) model Another interesting methodology combines regime Markov switching models and copulas. We want to introduce an approach to modeling dependence between financial returns allowing for two time-varying structures: we keep fixed one copula function across the two regimes characterizing equity markets, choosing between two copula forms. An alternative to this approach is the one proposed by Rodriguez (2007), which assumes time variation in the functional form of the copula. See Furman et al (2016), where the authors urge that the classical measures of tail dependence may underestimate the level of tail dependence in copulas
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