Dependence in credit default swap and equity markets: Dynamic copula with Markov-switching

Theoretical credit risk models à la Merton (1974) predict a non-linear negative link between the default likelihood and asset value of a firm. This motivates us to propose a flexible empirical Markov-switching bivariate copula that allows for distinct time-varying dependence between credit default swap (CDS) spreads and equity prices in “crisis” and “tranquil” periods. The model identifies high-dependence regimes that coincide with the recent credit crunch and the European sovereign debt crises, and is supported by in-sample goodness-of-fit criteria relative to nested copula models that impose within-regime constant dependence or no regime-switching. Value-at-Risk forecasts that aim to set day-ahead trading limits for the hedging of CDS-equity portfolios reveal the economic relevance of the model from the viewpoints of both regulatory and asymmetric piecewise linear loss functions.