Haar Wavelets-based Approach for Quantifying Credit Portfolio Losses

by Josep J. Masdemont of the Universitat Politècnica de Catalunya, and
Luis Ortiz-Gracia of the Centre de Recerca Matemàtica

April 2011

Abstract: This paper proposes a new methodology to compute Value at Risk (VaR) for quantifying losses in credit portfolios. We approximate the cumulative distribution of the loss function by a finite combination of Haar wavelet basis functions and calculate the coefficients of the approximation by inverting its Laplace transform. The Wavelet Approximation (WA) method is specially suitable for non-smooth distributions, often arising in small or concentrated portfolios, when the hypothesis of the Basel II formulas are violated. To test the methodology we consider the Vasicek one-factor portfolio credit loss model as our model framework. WA is an accurate, robust and fast method, allowing to estimate VaR much more quickly than with a Monte Carlo (MC) method at the same level of accuracy and reliability.

JEL Classification: C63, G21.

Keywords: Wavelets, Credit risk, VaR, Credit Portfolio, Quantitative Finance.

Forthcoming in: Quantitative Finance.

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