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Abstract
In this work, we propose a non-parametric density estimation technique for measuring the risk in a credit portfolio. The novel method is based on wavelets, and we derive closed-form expressions to calculate the Value-at-Risk (VaR), the Expected Shortfall (ES) as well as the risk contributions to VaR (VaRC) and ES (ESC). We consider the multi-factor Gaussian and t-copula models for driving the defaults. The results obtained along the numerical experiments show the impressive accuracy and speed of this method when compared with crude Monte Carlo simulation. The methodology presented applies in the same manner regardless of the model used, and the computational performance is invariant under a considerable change in the dimension of the model selected. The speed-up with respect to the classical Monte Carlo approach ranges from twenty-five to one-thousand depending on the model used.

Keywords: Risk Management, Value-at-Risk, Expected Shortfall, Portfolio Credit Risk Contributions, Shannon Wavelets