Regulatory Capital Modelling for Credit Risk

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 modelling 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 compact proof of this proposition under weaker assumptions. The IRB approach implements the so-called asymptotic single risk factor (ASRF) model, an asset value factor model of credit risk. The robustness of the model specification of the IRB approach to a relaxation in model assumptions is evaluated on a portfolio that is representative of the 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; and we evaluate the sensitivity of credit risk capital to dependence structure as modelled by asset correlations and elliptical copulas. A separate time series analysis takes measurements from the ASRF model of the prevailing state of Australia's economy and the level of capitalisation of its banking sector. These readings find general agreement with macroeconomic indicators, financial statistics and external credit ratings. However, given the range of economic conditions, from mild contraction to moderate expansion, experienced in Australia since the implementation of Basel II, we cannot attest to the validity of the model specification of the IRB approach for its intended purpose of solvency assessment. With the implementation of Basel II preceding the time when the effect of the financial crisis of 2007-09 was most acutely felt, our empirical findings offer a fundamental assessment of the impact of the crisis on the Australian banking sector. Access to internal bank data collected by the prudential regulator distinguishes our research from other empirical studies on the IRB approach and recent crisis

Assessing the Basel II Internal Ratings-Based Approach: Empirical Evidence from Australia

The Basel II internal ratings-based (IRB) approach to capital adequacy for credit risk implements an asymptotic single risk factor (ASRF) model. Measurements from the ASRF model of the prevailing state of Australia's economy and the level of capitalisation of its banking sector find general agreement with macroeconomic indicators, financial statistics and external credit ratings. However, given the range of economic conditions, from mild contraction to moderate expansion, experienced in Australia since the implementation of Basel II, we cannot attest to the validity of the model specification of the IRB approach for its intended purpose of solvency assessment. With the implementation of Basel II preceding the time when the effect of the financial crisis of 2007-09 was most acutely felt, our empirical findings offer a fundamental assessment of the impact of the crisis on the Australian banking sector. Access to internal bank data collected by the prudential regulator distinguishes our research from other empirical studies on the IRB approach and recent crisis.Comment: Addressed critiques of the Basel II IRB approach in the literature and updated figures, as well as general editing to tighten the pros

Regulatory Capital Modelling for Credit Risk

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.Comment: Updated figures and references to theorems/laws, as well as general editing to tighten the prose. arXiv admin note: text overlap with arXiv:1412.006