Analysis of credit portfolio risk using hierarchical multifactor models

ABSTRACT In this paper, we generalize Vasicek's asymptotic single-risk factor solution to multiple factors organized with a particular hierarchical structure. We use this model to investigate credit portfolio loss. In this hierarchical factor model, the asset returns of a company depend on a global factor, a sector factor and an idiosyncratic risk factor. All companies share the same global factor and all companies within a sector share the same sector factor. Using the central limit theorem, we derive closed-form solutions for the value-at-risk (VaR) and expected shortfall under the assumption that the number of sectors in the portfolio is large and the exposures scale is the reciprocal of the number of sectors. Our results for the VaR agree with Monte Carlo simulations, provided the sector factor loadings and variance of systematic risk are not too large. ;