Haar Wavelets-Based Approach for Quantifying Credit Portfolio Losses

TL;DR

This paper introduces a Haar wavelet-based method for efficiently and accurately computing Value at Risk in credit portfolios, especially effective for small or concentrated portfolios where traditional assumptions may fail.

Contribution

The paper presents a novel Haar wavelet approach to approximate loss distributions and compute VaR quickly, even under non-standard portfolio conditions.

Findings

Method is fast and accurate for small portfolios

Requires only a few wavelet coefficients for computation

Robust to violations of Basel II assumptions

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.