Failure of Saddle-point Method in the Presence of Double Defaults

We show that the saddle-point approximation method to quantify the impact of undiversified idiosyncratic risk in a credit portfolio is inappropriate in the presence of double default effects. Specifically, we prove that there does not exist an equivalent formula to the granularity adjustment, that accounts for guarantees, in case of the extended single-factor CreditRisk model. Moreover, in case of the model underlying the double default treatment within the internal ratings based (IRB) approach of Basel II, the saddle-point equivalent to the GA is too complex and involved to be competitive to a standard Monte Carlo approach.