Abstract
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.
Similar content being viewed by others
References
Yamanaka S, Sugihara M, Nakagawa H: Analysis of credit event impact with self-exciting intensity model. JSIAM Lett. 3, 49–52 (2011)
Martin, R., Thompson, K., Browne, C.: Taking to the saddle. RISK 14(9), 1–4 (2001)
Muromachi Y: A conditional independence approach for portfolio risk evaluation. J. Risk 7(1), 27–53 (2004)
Glasserman P, Ruiz-Mata J: Computing the credit loss distribution in the Gaussian copula model: a comparison of methods. J. Credit Risk 2, 33–66 (2007)
Takano, Y., Hashiba, J.: A novel methodology for credit portfolio analysis: numerical approximation approach. www.defaultrisk.com
Masdemont, J.J., Gracia, L.O.: Haar wavelets-based approach for quantifying credit portfolio losses. Quantitative Finance doi:10.1080/14697688.2011.595731
Gracia, L.O.; Masdemont, J.J.: Credit risk contributions under the Vasicek one-factor model : a fast wavelet expansion approximation. www.defaultrisk.com
Walter GG: Wavelets and Other Orthogonal Systems with Applications. CRC Press, Inc., Boca Raton (1994)
Ishitani K: A fast wavelet expansion technique for Vasicek multi-factor model of portfolio credit risk. JSIAM Lett. 4, 13–16 (2012)
Tasche, D.: Risk Contributions and Performance Measurement. Working paper, Munich University of Technology, Munich (2000)
Wynn P: On a device for computing the e m (S n ) transformation. Math. Tables Aids Comput. 10, 91–96 (1956)
Emmer S, Tasche D: Calculating credit risk capital charges with the one-factor model. J. Risk 7(2), 85–101 (2005)
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was supported by a grant-in-aid from Zengin Foundation for Studies on Economics and Finance.
About this article
Cite this article
Ishitani, K. A fast wavelet expansion technique for evaluation of portfolio credit risk under the Vasicek multi-factor model. Japan J. Indust. Appl. Math. 31, 1–24 (2014). https://doi.org/10.1007/s13160-013-0130-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13160-013-0130-4
Keywords
- Vasicek multi-factor model
- Haar wavelets
- Finite series expansion
- Wynn’s epsilon algorithm
- Cubic spline interpolation