Treatment of double default effects within the granularity adjustment for Basel II

Within the Internal Ratings-Based (IRB) approach of Basel II it is assumed that idiosyncratic risk has been fully diversified away. The impact of undiversified idiosyncratic risk on portfolio Value-at-Risk can be quantified via a granularity adjustment (GA). We provide an analytic formula for the GA in an extended singlefactor CreditRisk setting incorporating double default effects. It accounts for guarantees and their effect of reducing credit risk in theportfolio. Our general GA very well suits for application under Pillar 2 of Basel II as the data inputs are drawn from quantities already required for the calculation of IRB capital charges. -- analytic approximation ; Basel II ; counterparty risk ; double default ; granularity adjustment ; IRB approach ; securitization