A dimension reduction approach for loss valuation in credit risk modelling

TL;DR

This paper introduces a Bayesian filter-based dimension reduction technique for more accurate and efficient loss valuation in credit risk models, outperforming PCA in estimating expected loss and value-at-risk.

Contribution

It proposes a novel Bayesian filter and smoother approach for dimension reduction in credit risk loss valuation, improving accuracy and computational speed.

Findings

Outperforms PCA in estimating expected loss

Provides more accurate value-at-risk estimates

Offers a robust, easily implementable methodology

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 modelling, 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 is illustrated by numerical experiments. The results suggest that, compared to the currently most used PCA approach, the proposed methodology provides more accurate estimation of expected loss and value-at-risk of a loss distribution.