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FRM Part II · FRM Exam Part II · Credit Value Adjustment

A bank computes unilateral CVA on a 2-year swap with annual buckets. Discounted expected positive exposure is USD 4.0 million at year 1 and USD 5.0 million at year 2. Marginal default probabilities are 2% in year 1 and 3% in year 2. Recovery rate is 40%. Exposure and default are independent. What is the CVA?

CVA equals LGD of 60% times the sum of discounted exposure times marginal default probability: 0.6 times (4.0×2% + 5.0×3%) = 0.6 × 0.23 = USD 0.138 million. Forgetting the loss given default scaling gives 0.230, and using recovery instead gives 0.092.

  1. AUSD 0.138 millionCorrect
  2. BUSD 0.230 million
  3. CUSD 0.092 million
  4. DUSD 0.150 million

Explanation

Sum of discounted EPE times PD: 4.0*0.02 = 0.08; 5.0*0.03 = 0.15; total 0.23. Multiply by LGD 60%: 0.138. Omitting LGD gives 0.230. Using recovery 40% as the loss gives 0.092.

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