Haar wavelets-based approach for quantifying credit portfolio losses |
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Authors: | Josep J Masdemont Luis Ortiz-Gracia |
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Institution: | 1. Departament de Matemàtica Aplicada I , Universitat Politècnica de Catalunya , Diagonal 647, 08028 , Barcelona , Spain josep@barquins.upc.edu;3. Centre de Recerca Matemàtica , Campus de Bellaterra, Edifici C , 08193 Bellaterra, (Barcelona) , Spain |
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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 particularly 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 the estimation of the VaR much more quickly than with a Monte Carlo (MC) method at the same level of accuracy and reliability. |
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Keywords: | Wavelets in finance Value at Risk Portfolio management Credit risk Quantitative finance techniques Mathematical finance Risk measures |
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