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

A bank uses a simple discrete CVA formula: CVA = LGD × Σ discounted EE × marginal PD. A counterparty has a recovery rate of 40%. Over three one-year periods, the discounted expected exposures are USD 10 million, USD 12 million and USD 8 million, and the marginal default probabilities are 2%, 3% and 4% respectively. What is the CVA?

CVA equals loss given default of 60% multiplied by the sum of discounted exposure times marginal default probability. That sum is 0.88 million, so CVA is about USD 0.528 million, closest to USD 0.52 million. Forgetting the LGD factor would wrongly give USD 0.88 million.

  1. AUSD 0.5 million
  2. BUSD 0.6 million
  3. CUSD 0.52 millionCorrect
  4. DUSD 0.88 million

Explanation

LGD = 1 − 40% = 60%. Sum of EE × PD = 10×0.02 + 12×0.03 + 8×0.04 = 0.20 + 0.36 + 0.32 = 0.88. CVA = 0.6 × 0.88 = 0.528, about USD 0.53 million, which is closest to USD 0.52 million in the options only if rounded down; the exact value is 0.528. The 0.88 option omits LGD.

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