A fast wavelet expansion technique for evaluation of portfolio credit risk under the Vasicek multi-factor model

This paper presents a new methodology to compute value at risk (VaR) and the marginal VaR contribution (VaRC) in the Vasicek multi-factor model of portfolio credit loss. The wavelet approximation method can be useful to compute non-smooth distributions, often arising in small or concentrated portfol...

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Bibliographic Details
Published in:Japan journal of industrial and applied mathematics Vol. 31; no. 1; pp. 1 - 24
Main Author: Ishitani, Kensuke
Format: Journal Article
Language:English
Published: Tokyo Springer Japan 01.02.2014
Springer Nature B.V
Subjects:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Mathematics
Mathematics and Statistics
Original Paper
Wynn’s epsilon algorithm
Finite series expansion
Vasicek multi-factor model
Cubic spline interpolation
60E10
Haar wavelets
ISSN:0916-7005, 1868-937X
Online Access:Get full text
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Summary:This paper presents a new methodology to compute value at risk (VaR) and the marginal VaR contribution (VaRC) in the Vasicek multi-factor model of portfolio credit loss. The wavelet approximation method can be useful to compute non-smooth distributions, often arising in small or concentrated portfolios. This paper contributes to this technique by extending the wavelet approximation method for the Vasicek one-factor model to the multi-factor model. Key features of the new algorithm presented in this paper are (i) a finite series expansion of the wavelet scaling coefficients, (ii) fast calculation methods to accelerate convergence of those series and (iii) an efficient spline interpolation method to calculate the Laplace transforms. This paper also illustrates the effectiveness of the algorithm through numerical examples.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0916-7005
1868-937X
DOI:10.1007/s13160-013-0130-4