We apply a Coupled Markov Chain approach to model rating transitions and
thereby default probabilities of companies. We estimate parameters by applying
a maximum likelihood estimation using a large set of historical ratings. Given
the parameters the model can be used to simulate scenarios for joint rating
changes of a set of companies, enabling the use of contemporary risk management
techniques. We obtain scenarios for the payment streams generated by CDX
contracts and portfolios of such contracts.
There exists a range of different models for estimating and simulating credit
risk transitions to optimally manage credit risk portfolios and products. In
this chapter we present a Coupled Markov Chain approach to model rating
transitions and thereby default probabilities of companies. As the likelihood
of the model turns out to be a non-convex function of the parameters to be
estimated, we apply heuristics to find the ML estimators.