Optimizing Credit Risk Mitigation Effects of Collaterals Under Basel II

Abstract

One of the main differences in measuring capital requirements for credit risk due to the Internal Ratings Based Approach (IRBA) of the new regulatory Capital Standards (Basel II) is the enlarged acceptance of collaterals in order to reduce (supervisory) credit risk. Whereas in the Advanced IRBA own models for estimating the effects of collaterals can be used, in the Foundation IRBA concrete formulas are given. However, these regulations only explain the case of a single claim collateralized by a single asset or guarantee. If numerous collaterals are available for multiple loans, we receive an allocation problem of collaterals to loans with the objective of keeping regulatory capital low. In this article we model the corresponding optimization problem. Since numerical standard procedures often converge towards the wrong local minimum, we show how to apply evolutionary algorithms as well as simulated annealing.