Chapter 5 - Migration Matrices and the Markov Chain Approach

Abstract

This chapter describes the model and its relevance for determining risk-neutral migration matrices. It concentrates on the definition and properties of discrete and continuous-time transition matrices. A continuous time Markov chain can also model credit migration. Therefore, it introduces the idea of generator matrices and continuous-time modeling of rating transitions. The construction of credit curves provides information about cumulative default rates. Using generator matrices, it is also possible to obtain transition matrices for arbitrary time horizons. The continuous time framework also permits to generate confidence sets for default probabilities in higher rating classes. In the continous-time approach it does not have to worry which yearly periods we consider. Using a discrete-time approach may lead to quite different results depending on the starting point of consideration.