Journal of Risk

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Failure of the saddlepoint method in the presence of double defaults

Eva Lütkebohmert

ABSTRACT

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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