A dynamic default dependence model

We develop a dynamic multivariate default model for a portfolio of credit-risky assets in which default times are modelled as random variables with possibly different marginal distributions, and L�vy subordinators are used to model the dependence among default times. In particular, we define a cumulative dynamic hazard process as a L�vy subordinator, which allows for jumps and induces positive probabilities of joint defaults. We allow the main asset classes in the portfolio to have different cumulative default probabilities and corresponding different cumulative hazard processes. Under this heterogeneous assumption we compute the portfolio loss distribution in closed form. Using an approximation of the loss distribution, we calibrate the model to the tranches of the iTraxx Europe. Once the multivariate default distribution has been estimated, we analyse the distress dependence in the portfolio by computing indicators of systemic risk, such as the Stability Index, the Distress Dependence Matrix and the Probability of Cascade Effects.