Multivariate markov chain model for credit risk measurement

Abstract

The aim of the study is to use a multivariate Markov model to simulate the dynamics of correlated credit ratings of multiple firms. Credibility theory is used to get the weighting used to estimate the transition matrix and other unknown model parameters in the multivariate Markov chain model. The study presents a higher-order Markov chain models for forecasting the various credit risk rating dynamics. The results are transition matrices from various risk ratings. The most important step in analyzing data is the selection of an appropriate mathematical model for the data as it helps in predictions and hypothesis testing. The research design used for the study was a descriptive research design that basically involves obtaining information concerning the current status of the phenomena to describe, "What exists" with respect to variables or conditions in a situation Gardner et al (2004). This design was appropriate for this study, as it . gave the relevant information as it was. The traditional reduced-form approach assumes that the losses from a credit risk at each particular rating class can be evaluated based on accounting information and principles. With the data entered and parameters estimated, a prediction table of transition probabilities from one grade to another was created which indicated that the Ching et al (2002) model follows a 3rd order polynomial to be able to come up with the transition matrices. In conclusion the transition matrices were estimated by the use of a linear combination of the empirical transition matrix and prior estimate of the transition matrix. By incorporating both the historical rating data and another source of information about rating data which includes expert opinion or subjective views, one is able to come up with the next period's rating of a particular credit risk to that depends on its current rating and also the current ratings of other credit risks inthe portfolio.