Regulatory Capital Modelling for Credit Risk

TL;DR

This paper explores the mathematical foundations of the Basel II IRB approach for credit risk capital, extending the model beyond Gaussian assumptions and analyzing convergence and dependence sensitivity using Australian bank data.

Contribution

It generalizes the IRB model to broader settings, provides a weaker assumptions proof, and empirically evaluates convergence and dependence effects with real bank data.

Findings

Quantiles of conditional expectation can substitute for loss distribution quantiles.

Empirical loss distributions converge to the asymptotic distribution as obligors increase.

Credit risk capital sensitivity varies with asset correlations and copula choices.

Abstract

The Basel II internal ratings-based (IRB) approach to capital adequacy for credit risk plays an important role in protecting the Australian banking sector against insolvency. We outline the mathematical foundations of regulatory capital for credit risk, and extend the model specification of the IRB approach to a more general setting than the usual Gaussian case. It rests on the proposition that quantiles of the distribution of conditional expectation of portfolio percentage loss may be substituted for quantiles of the portfolio loss distribution. We present a more economical proof of this proposition under weaker assumptions. Then, constructing a portfolio that is representative of credit exposures of the Australian banking sector, we measure the rate of convergence, in terms of number of obligors, of empirical loss distributions to the asymptotic (infinitely fine-grained) portfolio loss distribution. Moreover, we evaluate the sensitivity of credit risk capital to dependence structure as modelled by asset correlations and elliptical copulas. Access to internal bank data collected by the prudential regulator distinguishes our research from other empirical studies on the IRB approach.