Dynamic Modeling of Portfolio Credit Risk with Common Shocks

We consider a bottom-up Markovian model of portfolio credit risk where dependence among credit names stems from the possibility of simultaneous defaults. A common shocks interpretation of the model is possible so that efficient convolution recursion procedures are available for pricing and hedging CDO tranches, conditionally on any given state of the Markov 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. As a result this model allows us to hedge CDO tranches using singlename CDS-s in a theoretically sound and practically convenient way. To illustrate this we calibrate the model against market data on CDO tranches and the underlying singlename CDS-s. We then study the loss distributions as well as the min-variance hedging strategies in the calibrated portfolios.