Summary
The CreditRisk+ model is described in terms of characteristic functions, and two methods to determine the distribution of the credit loss based on Fourier inversion are presented. For the convenience of the reader, a short introduction to the theory of characteristic functions and the Fourier transformation is given. Then two general results are stated how to obtain the distribution of a random variable from its characteristic function. These general techniques, which are based on Fourier inversion, will be applied to the CreditRisk+ model and yield efficient and numerically stable algorithms, which provide the loss distribution in the CreditRisk+ framework. Advantages of this approach are that the algorithms are easy to implement and that a basic loss unit is not required.
Supported by the DFG Research Center “Mathematics for key technologies” (FZT 86) in Berlin.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Abramowitz and I. A. Stegun (eds.). Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables. Dover Publications, Inc., New York, ninth printing, 1972.
P. Bürgisser, A. Kurth, and A. Wagner. Incorporating severity variations into credit risk. Journal of Risk, 3 (4): 5–31, 2001.
Credit Suisse Financial Products. CreditRisk+: A credit risk management framework. London, 1997. Available at http://www.csfb.com/creditrisk.
W. Feller. An Introduction to Probability Theory and Its Applications, Wiley Series in Probability and Mathematical Statistics, John Wiley Sons, Inc. New York. Volume I, Third Edition, 1968 — Volume II, 1966.
G. Giese. Enhancing CreditRisk+. Risk, 16 (4): 73–77, 2003.
M. B. Gordy. Saddlepoint approximation of CreditRisk+. Journal of Banking Finance, 26: 1335–1353, 2002.
W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery. Numerical Recipes in C: The Art of Scientific Computing. Second Edition, Cambridge University Press, Cambridge, 1992.
O. Reìß. Fourier inversion algorithms for generalized CreditRisk+ models and an extension to incorporate market risk. WIAS—Preprint No. 817, 2003.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Reiß, O. (2004). Fourier Inversion Techniques for CreditRisk+ . In: Gundlach, M., Lehrbass, F. (eds) CreditRisk+ in the Banking Industry. Springer Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06427-6_8
Download citation
DOI: https://doi.org/10.1007/978-3-662-06427-6_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05854-7
Online ISBN: 978-3-662-06427-6
eBook Packages: Springer Book Archive