Asymmetric Dependence Patterns in Financial Time Series

Abstract

This paper proposes a new copula-based approach to test for asymmetries in the dependence structure of financial time series. Simply splitting observations into subsamples and comparing conditional correlations leads to spurious results due to the well-known conditioning bias. Our suggested framework is able to circumvent these problems. Applying our test to market data, we statistically confirm the widespread notion of significant asymmetric dependence structures between daily changes of the VIX, VXN, VDAXnew, and VSTOXX volatility indices and their corresponding equity index returns. A maximum likelihood method is used to perform a likelihood ratio test between the ordinary t-copula and its asymmetric extension. To the best of our knowledge, our study is the first empirical implementation of the skewed t-copula to generate meta skewed student t-distributions. Its asymmetry leads to significant improvements in the description of the dependence structure between equity returns and implied volatility changes.