A dimension reduction approach for loss valuation in credit risk modeling

Abstract

This paper addresses the “curse of dimensionality” in the loss valuation of credit risk models. A dimension reduction methodology based on the Bayesian filter and smoother is proposed. This methodology is designed to achieve a fast and accurate loss valuation algorithm in credit risk modeling, but it can also be extended to valuation models of other risk types. The proposed methodology is generic, robust and can easily be implemented. Moreover, the accuracy of the proposed methodology in the estimation of expected loss and value-at-risk (VaR) is illustrated by numerical experiments. The results suggest that, compared to the currently most used Principal Component Analysis (PCA) approach, the proposed methodology provides more accurate estimation of expected loss and VaR of a loss distribution.