Abstract
This work aims to illustrate an advanced quantitative methodology for measuring the credit risk of a loan portfolio allowing for diversification effects. Also, this methodology can allocate the credit capital coherently to each counterparty in the portfolio. The analytical approach used for estimating the portfolio credit risk is a binomial type based on a Monte Carlo Simulation. This method takes into account the default correlations among the credit counterparties in the portfolio by following a copula approach and utilizing the asset return correlations of the obligors, as estimated by rigorous statistical methods. Moreover, this model considers the recovery rates as stochastic and dependent on each other and on the time until defaults. The methodology utilized for coherently allocating credit capital in the portfolio estimates the marginal contributions of each obligor to the overall risk of the loan portfolio in terms of Expected Shortfall (ES), a risk measure more coherent and conservative than the traditional measure of Value-at-Risk (VaR). Finally, this advanced analytical structure is implemented to a hypothetical, but typical, loan portfolio of an Italian commercial bank operating across the overall national country. The national loan portfolio is composed of 17 sub-portfolios, or geographic clusters of credit exposures to 10,500 non-financial firms (or corporates) belonging to each geo-cluster or sub-portfolio. The outcomes, in terms of correlations, portfolio risk measures and capital allocations obtained from this advanced analytical framework, are compared with the results found by implementing the Internal Rating Based (IRB) approach of Basel II and III. Our chief conclusion is that the IRB model is unable to capture the real credit risk of loan portfolios because it does not take into account the actual dependence structure among the default events, and between the recovery rates and the default events. We underline that the adoption of this regulatory model can produce a dangerous underestimation of the portfolio credit risk, especially when the economic uncertainty and the volatility of the financial markets increase.
Highlights
The financial system has become more volatile due to increasing globalization and financial integration
From the outcomes of this work, the strong underestimation of portfolio credit risk produced by the Internal Rating Based (IRB) model is evident, given its restrictive underlying hypotheses
When we drop the assumption of highly diversified portfolios, the estimates of the portfolio risk measures obtained by implementing the advanced quantitative methodology increase significantly
Summary
The financial system has become more volatile due to increasing globalization and financial integration. The approach utilized for allocating credit capital coherently (Overbeck 2000; Denault 2001; Kalkbrener et al 2004; Kalkbrener 2005) estimates the marginal contributions of each obligor to the overall risk of the loan portfolio in terms of Expected Shortfall (ES), a risk measure that is coherent (in sense of Artzner et al 1999; Tasche 2002; Acerbi and Tasche 2002) and more conservative than the traditional measure of Value-at-Risk (VaR) This advanced analytical structure is implemented to a hypothetical but typical loan portfolio of an Italian commercial bank operating across the country. This binomial (default/non-default) model is based on Monte Carlo Simulation, and takes into account the default correlations among obligors in the portfolio, following the idea of the copula approach first developed by Li (2000).
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