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FRM Part II · FRM Exam Part II · Credit Derivatives

A bank buys CDS protection on a loan from a counterparty. The reference entity and the counterparty have independent defaults, with one-year default probabilities of 4% for the reference entity and 2% for the protection seller. Ignoring recovery on the seller and any timing issues, what is the probability that the bank is left unprotected after a reference entity default, i.e. both default over the year?

The probability is 0.08%. Under independence the joint default probability is the product of the two individual probabilities, 4% times 2%. This is much smaller than either single default probability, which is why protection from an uncorrelated seller is valuable.

  1. A0.08%Correct
  2. B2.00%
  3. C4.00%
  4. D5.92%

Explanation

With independence, joint default probability is 4% x 2% = 0.08%. The 5.92% option is the union probability (4+2-0.08), which is the chance at least one defaults, not both. The 2% and 4% options are single-name probabilities.

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