Ricerc@Sapienza

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.