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Predictions Based on Certain Uncertainties - A Bayesian Credit Portfolio Approach

by Christoff Gössl of HypoVereinsbank AG

July 14, 2005

Abstract: The analysis of default probabilities and correlations within credit risky portfolios is usually strongly affected by the scarce availability of data. High standard deviations and a fair amount of uncertainty in the derived estimates are well known consequences of this. However, when deriving predictions in a second stage these volatilities are usually ignored and only point estimators are used, giving a false appearance of accuracy. The aim of this paper is to show how a consideration of these uncertainties will affect this second stage analysis. Besides the introduction of a new Bayesian credit portfolio approach, for this purpose in a Bayesian framework the joint posterior distribution of default probabilities and correlation parameters will be derived. Further, the effects are quantified a consideration of this distribution would have, with respect to the prediction of portfolio risk figures and also for pricing of structured derivatives.

Keywords: Credit risk, Bayes, MCMC.

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