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Credit Portfolio Risk and PD Confidence Sets through the Business Cycle

by Stefan Trück of the Universität Karlsruhe, and
Svetlozar T. Rachev of the Universität Karlsruhe & the University of California, Santa Barbara

May 31, 2005

Abstract: Transition matrices are an important determinant for risk management and VaR calculations in credit portfolios. It is well known that rating migration behavior is not constant through time. It shows cyclicality and significant changes over the years. We investigate the effect of changes in migration matrices on credit portfolio risk in terms of Expected Loss and Value-at-Risk figures for exemplary loan portfolios. The estimates are based on historical transition matrices for different time horizons and a continuous-time simulation procedure. We further determine confidence sets for the probability of default (PD) in different rating classes by a bootstrapping methodology. Our findings are substantial changes in VaR as well as for the width of estimated PD confidence intervals.

Keywords: Credit VaR, Transition Matrices, Rating Migration, Business Cycle, Continuous-time Modeling, PD estimation

Published in: Journal of Credit Risk, Vol. 1. No. 4, (Fall 2005), pp. 61-88.

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