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Simulating Historical Ratings Transition Matrices for Credit Risk Analysis in Mathematica

by Mark S. Coleman of the Chatham Research Alliance

October 28, 2002

Abstract: Quantitative methods for evaluating credit risk have gained increasing importance the past several years. Many of the most common analytical credit risk procedures use historical ratings transition matrices published by the three major U.S. rating agencies. In many cases, however, the specific approaches used are too limiting in that the observed historical variation in the Markov transition probabilities is not fully utilized to evaluate the risk of portfolios of credit instruments. We argue that this variation, which in part is caused by changes in the underlying economic and financial factors that determine credit market behavior, is an important element of true underlying risk of these financial instruments. This paper uses Mathematica to present an approach for simulating ratings transitions that accounts for the underlying variation in credit transition behavior. We use a copula-based Monte Carlo approach to help account for the historical cross-correlation of ratings probability changes over a 20-year sample of data spanning 1981-2000.

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