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FRM Part II · FRM Exam Part II · Credit Derivatives

A first-to-default (FTD) basket CDS references five names. Holding individual default probabilities fixed, how does an increase in the default correlation among the names affect the FTD spread and the spread on a last-to-default (n-th to default, n=5) basket?

Higher default correlation lowers the first-to-default spread and raises the last-to-default spread. Defaults cluster, so the chance of at least one default falls while the chance of all names defaulting rises, given unchanged individual default probabilities.

  1. AFTD spread decreases; last-to-default spread increasesCorrect
  2. BFTD spread increases; last-to-default spread decreases
  3. CBoth spreads increase
  4. DBoth spreads decrease

Explanation

With higher correlation, defaults cluster, so the probability that at least one name defaults falls, lowering the FTD spread. The probability that all five default rises, raising the last-to-default spread. The opposite signs arise because the two products load on opposite tails of the joint default distribution.

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