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FRM Part II · FRM Exam Part II · Credit Derivatives

An investor buys a first-to-default (FTD) basket swap referencing five names with identical individual default probabilities and a positive default correlation. If the pairwise default correlation among the names rises, with individual CDS spreads unchanged, what is the most likely effect on the fair FTD spread?

The fair first-to-default spread falls. Higher correlation makes defaults cluster in the same scenarios, which lowers the probability that at least one name defaults. The FTD spread is highest at zero correlation, where it approaches the sum of the single-name spreads, and falls as correlation rises.

  1. AIt rises, because higher correlation increases the chance that at least one name defaults
  2. BIt falls, because defaults cluster so the probability of at least one default declinesCorrect
  3. CIt is unchanged, because individual default probabilities are unchanged
  4. DIt rises, because the loss given default of the first defaulter increases

Explanation

With higher correlation, defaults cluster in the same scenarios, so the probability that at least one name defaults falls toward the probability of a single name defaulting. With zero correlation the chance of at least one default is highest. The FTD spread therefore falls as correlation rises, and it is bounded above by the sum of the individual spreads. Option 0 reverses this relationship.

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