FRM Part II · FRM Exam Part II · Derivatives
A bank computes unilateral CVA on a 3-year swap using annual buckets. Discounted expected positive exposures at years 1, 2 and 3 are USD 2.0 million, 3.0 million and 2.0 million. Marginal risk-neutral default probabilities for the counterparty in years 1, 2 and 3 are 1%, 2% and 3%. Recovery rate is 40%. Ignoring wrong-way risk, what is the CVA?
CVA is LGD times the sum of discounted EPE multiplied by marginal default probability. The sum is 0.14 million, and with 60% LGD the CVA is USD 0.084 million. Forgetting to apply LGD gives the incorrect 0.140 million.
- AUSD 0.084 millionCorrect
- BUSD 0.140 million
- CUSD 0.050 million
- DUSD 0.196 million
Explanation
Sum of EPE x PD = 2.0(0.01) + 3.0(0.02) + 2.0(0.03) = 0.02 + 0.06 + 0.06 = 0.14 million. Multiply by LGD of 60%: 0.14 x 0.6 = 0.084 million. Option 0.140 omits the loss given default factor.
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