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Efficient Monte Carlo Methods for Convex Risk Measures in Portfolio Credit Risk Models

by Jörn Dunkel of the Max-Planck-Institute, and
Stefan Weber of Cornell University

August 25, 2005

Abstract: We discuss efficient Monte Carlo methods for the estimation of convex risk measures in portfolio credit risk models. We focus on the Utility-based Shortfall Risk measures (SR). These risk measures do not share the deficiencies of the current industry standard Value at Risk (VaR). The analysis of large financial losses in realistic portfolio models requires extensive numerical simulations. In the present paper we demonstrate that importance sampling with an exponential twist can be used to construct numerically efficient estimators for SR within the framework of the credit risk models CreditRisk+ and CreditMetrics. Numerical simulations of test portfolios demonstrate the good performance of the proposed estimators.

Keywords: Portfolio credit risk management, convex risk measures, shortfall risk, importance sampling.

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