Hermite Approximations in Credit Portfolio Modeling with Probability of Default-Loss Given Default Correlation

In this paper, we propose a novel multifactor analytic framework for credit portfolio modeling that incorporates the impact of the probability of default-loss given default correlation. In particular, we provide explicit expressions for calculating volatility, value-at-risk and expected shortfall, along with the associated Euler risk contributions. This approach is an extension and application of the framework proposed by Voropaev in 2011 and Buet-Golfouse and Owen in 2015. The main intended application is for large loan or mortgage portfolios, and as such we neglect idiosyncratic risk adjustments. This simplifies the expressions and improves computational speed. We finish by comparing the analytic results with a vanilla Monte Carlo implementation.