Journal of Risk

Failure of the saddlepoint method in the presence of double defaults

Eva Lütkebohmert


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

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