  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.
