FRM Part II · FRM Exam Part II · Derivatives
A bank has an unilateral CVA on a swap with a counterparty with a loss given default of 60%. Over three annual periods, the discounted expected positive exposures are 2.0 million, 3.0 million and 1.0 million, and the marginal default probabilities for the three years are 1%, 2% and 3%. Using the standard discretised formula, what is the CVA?
CVA equals LGD times the sum of discounted expected exposure multiplied by marginal default probability. The sum is 0.11 million, and with a 60% loss given default the CVA is 0.066 million. Forgetting to apply loss given default would wrongly give 0.11 million.
- A0.066 millionCorrect
- B0.072 million
- C0.060 million
- D0.110 million
Explanation
CVA = LGD x sum(EPE x marginal PD) = 0.6 x (2.0x0.01 + 3.0x0.02 + 1.0x0.03) = 0.6 x (0.02+0.06+0.03) = 0.6 x 0.11 = 0.066 million. The 0.110 value omits the LGD. Using 40% recovery as LGD would give 0.044.
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