Modelling Dependence in CDS and Equity Markets - Dynamic Copula with Markov-Switching

Our research extends existing knowledge on the non-linear relation between credit spreads and tradeable systematic risk factors by utilising copulas, which represent a very versatile framework to estimate multivariate distributions. A novel Markov-switching dynamic (autoregressive) copula model is advocated as a flexible way to capture extreme return clustering and asymmetry. The copula model proposed explicitly captures sudden shifts between low or "normal" and high or "crash" dependence regimes while allowing for mean-reversion in dependence within each regime. The empirical analysis conducted using a sample of daily observations over the period 2005 to 2012 reveals significant regime-switches in dependence between the iTraxx CDS index and the underlying Stoxx equity index, on the one hand, and the implied volatility VStoxx index, on the other. In particular, various episodes of heightened rank-correlations and tail-dependence are identified post-2006 broadly coinciding with the credit crunch, automotive sector crisis and the recent Greek and European sovereign debt crises. These results suggest that systematic factors play a stronger role as drivers of default during periods of stress. Markov-switching dynamic copula models are supported over simpler nested copulas not only by conventional in-sample statistical criteria but also by out-of-sample Value at Risk backtesting. Using regulatory loss functions that take into account the frequency and magnitude of exceptions, a Value at Risk simulation highlights the economic relevance of our copula models for risk managers and regulators by showing that they lead to more cautious 1-day-ahead trading limits.