Calculating Basel II Risk Parameters for a Portfolio of Retail Loans

Abstract

Under the Basel II regime, banks can choose among different approaches tomeasure the regulatory capital to underpin their risky assets. From the pointof view of the amount of capital required, the Retail IRB Approach can be veryadvantageous. To satisfy its requirements, banks have to estimate sensible valuesfor the risk parameters Probability of Default (PD) and Loss Given Default (LGD)on the basis of their own default and loss data. In part due to the segmentationrules particular to the Retail IRB Approach, this is very difficult, and the simplecalculation of relative frequencies will not do in general – the sample data do notallow one to make a sensible distinction between the structure of the default andloss densities and the randomness of the sample data, as we see in this thesis;all methods we derive for computing risk parameters are developed using realbank data.

We describe a method to estimate PD using the construction of a Lorenz curvebased on scoring results. While Lorenz curves usually are means to computeefficiency ratios, we show how a Lorenz curve can serve as a vehicle to define theborderline between structure and randomness. Values for PD can be obtainedfrom it in a direct way. What makes it specifically suitable for this purposeare some invariancy properties; we show this in general and by way of sampledata of a real retail portfolio.
We further compare this method to multivariatemethods, and propose a multi-component system to balance the complementaryadvantages and disadvantages of both approaches.Very often, there is no “LGD rating system” analogous to the PD rating, and so wederive values for LGD by observing so-called special provision cohorts over time.Making a special provision is part of the default definition, and by exponentiallymodelling the time behaviour of special provision volumes one can estimate valid LGD numbers, as we show in the relevant Chapter.

The last Chapter goes beyond Basel II. We assume the validity of the “Loss of Memory Property” for a typical retail portfolio, and show that borrower default under this assumption can be compared to radioactive decay. The mathematical modelling of decaying nuclei is transported to defaulting borrowers, from where some explicit formulae for Unexpected Loss are derived. As all terms of these formulae can be estimated from our sample portfolio data, this model can serve as a validation tool for an internal portfolio model.

This thesis sprang from Basel II project work in a medium-sized german bank. Four colleagues of mine and myself collaborated in problems closely related to the subject of this thesis, and so the thesis owes much to the many discussions we had. It is a pleasure to me to express my thanks to all of my colleagues: Dr Ulrike Volmar, Dr Vesselka Ivanova,Dr Christian Oehler, Dr Achim Steinbauer.

Freiburg, Germany, 12th of April 2003. Dr Peter Gloßner