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

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.