On the Applicability of Fourier Based Methods to Credit Portfolio Models with Integrated Interest Rate and Credit Spread Risk

by Peter Grundke of the University of Cologne

September 2005

Abstract: In this paper it is analyzed whether a Fourier based approach can be an efficient tool for calculating risk measures in the context of a credit portfolio model with integrated market risk factors. For this purpose, this technique is applied to a version of the well-known credit portfolio model CreditMetrics extended by correlated interest rate and credit spread risk. Unfortunately, the characteristic function of the credit portfolio value at the risk horizon can not be calculated in closed-form, but has to be computed by Monte Carlo simulations. Due to this drawback, in the considered numerical examples the performance of the Fourier based approach is not better than that of a full Monte Carlo simulation of the future credit portfolio distribution, especially for inhomogeneous portfolios and when percentiles corresponding to high confidence levels are needed. The application of standard Importance Sampling techniques for improving the performance of the Fourier based approach is problematic, too.

JEL Classification: C63, G21.

Keywords: credit risk, interest rate risk, credit spread risk, credit portfolio model, Value at Risk, characteristic function, Fourier transformation.

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Previously titled: Application of Fourier Inversion Methods to Credit Portfolio Models with Integrated Interest Rate and Credit Spread Risk

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