Dynamic Modeling of Portfolio Credit Risk with Common Shocks

We consider a bottom-up Markovian copula model of {portfolio} credit risk where instantaneous contagion is possible in the form of simultaneous defaults. Due to the Markovian copula nature of the model, calibration of marginals and dependence parameters can be performed separately using a two-steps procedure, much like in a standard static copula set-up. In this sense this model solves the bottom-up top-down puzzle which the CDO industry had been trying to do for a long time. It can be applied to any dynamic credit issue like consistent valuation and hedging of CDSs, CDOs and counterparty risk on credit portfolios.