Credit Migration Risk Modelling

We consider the modelling of credit migration risk and the pricing of migration derivatives. To construct a Point-in-Time (PIT) rating migration matrix as the underlying value for derivative pricing we show first that the Affine Markov Chain models is not sufficient to generate PIT migration matrices in both, an economic boom and contraction. We show that the introduction of rating direction and speed, which replace the ambiguous rating drift, and the use of a Regime Shifting Markov Mixture model both lead to migration matrices which fit well with Point-in-Time data. Our extended framework still provides an analytical pricing formula for CDS. We apply the model to price CDS before and during the current financial crisis. The results show a large underpricing in the CDS market prices compared to the theoretical prices before the the financial crises stared.