Don't Fall from the Saddle: The Importance of Higher Moments of Credit Loss Distributions

30 Pages Posted: 16 Jun 2007

See all articles by Jan Annaert

Jan Annaert

University of Antwerp Department of Accounting & Finance; University of Antwerp - Antwerp Management School

Joao Garcia

Fitch Solutions

Jeroen Lamoot

Banking, Finance and Insurance Commission (CBFA)

Gleb Lanine

Ghent University - Department of Financial Economics; Ghent University - Centre for Russian International Socio-Political and Economic Studies (CERISE)

Date Written: February 2007

Abstract

The original Panjer recursion of the CreditRisk+ model is said to be unstable and therefore to yield inaccurate results of the tail distribution of credit portfolios. A much-hailed solution for the flaws of the Panjer recursion is the saddlepoint approximation method. In this paper we show that the saddlepoint approximation is an accurate and robust tool only for credit portfolios with low skewness and kurtosis of the loss distribution. However, often credit portfolios are heterogeneous with large skewness and kurtosis. We show that for such portfolios the commonly applied saddlepoint approximations (the Lugannani-Rice and the Barndorff-Nielsen formulas) are not reliable. We explain it by the dependence of the high-order standardized cumulants and the relative error on the saddlepoint. The more the cumulants and the relative error fluctuate for variations in the value of the saddlepoint (from 0 to the upper bound) the less accurate the saddlepoint approximation is. Hence, the saddlepoint approximations are not a universal substitute to the Panjer recursion algorithm. We also provide users of CR+ with a set of diagnostics to identify beforehand when the saddlepoint approximations are prone to failure.

Keywords: CreditRisk+, saddlepoint approximations, Lugannani-Rice formula, Barndorff-Nielsen formula, credit VaR.

JEL Classification: G18, G21, G33

Suggested Citation

Annaert, Jan and Crispiniano Garcia, Joao Batista and Lamoot, Jeroen and Lanine, Gleb, Don't Fall from the Saddle: The Importance of Higher Moments of Credit Loss Distributions (February 2007). Available at SSRN: https://ssrn.com/abstract=994182 or http://dx.doi.org/10.2139/ssrn.994182

Jan Annaert

University of Antwerp Department of Accounting & Finance ( email )

Faculty of Applied Economics
Prinsstraat 13
Antwerp, B-2000
Belgium

HOME PAGE: http://https://www.uantwerp.be/en/staff/jan-annaert/

University of Antwerp - Antwerp Management School ( email )

Boogkeers 5
Antwerp, 2000
Belgium

Joao Batista Crispiniano Garcia

Fitch Solutions ( email )

United Kingdom

HOME PAGE: http://www.sergeandjoao.com

Jeroen Lamoot (Contact Author)

Banking, Finance and Insurance Commission (CBFA) ( email )

Brussels, B-1000
Belgium

Gleb Lanine

Ghent University - Department of Financial Economics ( email )

Ghent, 9000
Belgium

Ghent University - Centre for Russian International Socio-Political and Economic Studies (CERISE)

Gent, 9000
Belgium

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