Haar wavelets-based approach for quantifying credit portfolio losses

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 wavelets basis functions and calculate the coefficients of the approximation by inverting its Laplace transform. In fact, we demonstrate that only a few coefficients of the approximation are needed, so VaR can be reached quickly. To test the methodology we consider the Vasicek one-factor portfolio credit loss model as our model framework. The Haar wavelets method is fast, accurate and robust to deal with small or concentrated portfolios, when the hypothesis of the Basel II formulas are violated.

Quantifying Credit Portfolio Losses Under Multi-Factor Models

“…For this purpose, we use the metod initially developed in [12] for Laplace transform inversion and further extended in [15] for Fourier transform inversion, where numerical errors are studied in detail as well. It is based on Haar wavelets (for a deep insight in wavelets we refer the reader to [4]) and called WA.…”

“…We consider in Section 2.1 the multi-factor Gaussian copula model, which is the extension from one factor to several factors of model (2) treated in [12,14]. We consider the t-copula and multi-factor t-copula models in Section 2.2 and Section 2.3, respectively.…”

“…, N . The corresponding characteristic function is calculated as in [12], this is, following expression (8) for the one-dimensional case and solving the integral by means of Gauss-Hermite quadrature with 20 nodes. We plot the results in Figure 1.…”

“…We build upon the work in [12] where the one-factor Gaussian copula model was considered as the model framework and we tackle the more involved problem concerning multi-factor models. The one-factor model belongs to the class of structural models and it is a one period default model, i.e., loss only occurs when an obligor defaults in a fixed time horizon.…”

Efficient VaR and Expected Shortfall computations for nonlinear portfolios within the delta-gamma approach

“…We can apply a bisection method so that g VaR m ðaÞ can be calculated in at most m iterations (see [11] for details), yielding,…”