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FRM Part II · FRM Exam Part II · Credit Derivatives

A bank holds a USD 20 million loan to Firm X (default probability 4%) and buys CDS protection on Firm X from Dealer Y (default probability 2%). Assume the two defaults are independent and the protection is for the full USD 20 million with recovery on the reference obligation of 40%. Ignoring discounting and the premium, what is the probability the bank is left unprotected, meaning that X defaults and Y also defaults?

The probability is 0.08%. Under independence, the joint default probability is the product of the two individual probabilities, 4% times 2%. Adding them would give the chance of either defaulting, not both, which is what leaves the bank unprotected.

  1. A0.08%Correct
  2. B0.80%
  3. C2.00%
  4. D6.00%

Explanation

With independence, the joint probability is 4% x 2% = 0.08%. The 6% figure adds the probabilities, which is wrong because it measures either event and not both. The 0.80% figure comes from a decimal error.

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