Calculating credit risk capital charges with the one-factor model

TL;DR

This paper develops approximate analytical formulas for calculating credit risk capital charges in the one-factor model, aiming to reduce computational time compared to Monte Carlo simulations.

Contribution

It introduces two new approaches—granularity adjustment and semi-asymptotic—for analytical approximation of credit risk measures in the one-factor model.

Findings

Formulas enable faster credit risk calculations.

Numerical example demonstrates accuracy of the approaches.

Reduces reliance on computationally intensive simulations.

Abstract

Even in the simple one-factor credit portfolio model that underlies the Basel II regulatory capital rules coming into force in 2007, the exact contributions to credit value-at-risk can only be calculated with Monte-Carlo simulation or with approximation algorithms that often involve numerical integration. As this may require a lot of computational time, there is a need for approximate analytical formulae. In this note, we develop formulae according to two different approaches: the granularity adjustment approach initiated by M. Gordy and T. Wilde, and a semi-asymptotic approach. The application of the formulae is illustrated with a numerical example. Keywords: One-factor model, capital charge, granularity adjustment, quantile derivative.