Credit migration risk modeling

ABSTRACT We consider the modeling of credit-migration risk and the pricing of migration derivatives. To construct a point-in-time rating migration matrix as the underlying value for derivative pricing we first show that affine Markov chain models are not sufficient for generating point-in-time migration matrices in both an economic boom and an economic 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 that fit well with point-in-time data. Our extended framework still provides an analytical pricing formula for credit default swaps (CDSs).We use the model to price CDSs before and during the current financial crisis (2007-10). The results show a large underpricing in the CDS market prices when compared with the theoretical prices before the financial crisis began.