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FRM Part II · FRM Exam Part II · Credit Derivatives

A 5-year CDS has a notional of USD 50 million and a fair spread of 200 bps. The expected recovery rate is 40 percent. Using the approximation that spread equals annual default intensity times (1 - recovery), and treating the intensity as constant, what is the approximate annual risk-neutral default probability, and the approximate probability of surviving 5 years using continuous compounding (e^-5h)?

The annual default intensity is the spread divided by loss given default: 2 percent over 60 percent, about 3.33 percent. Five-year survival is exp(-5 x 0.0333), about 84.6 percent. Using the 2 percent spread directly ignores recovery and understates default probability.

  1. AAnnual about 3.33 percent; 5-year survival about 84.6 percentCorrect
  2. BAnnual about 2.00 percent; 5-year survival about 90.5 percent
  3. CAnnual about 5.00 percent; 5-year survival about 77.9 percent
  4. DAnnual about 3.33 percent; 5-year survival about 90.5 percent

Explanation

h = 0.02 / (1 - 0.40) = 0.0333. Survival over 5 years = exp(-0.1667) = 0.846. Using the spread alone (2 percent) ignores recovery and gives 90.5 percent survival; dividing by recovery gives 5 percent.

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