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Answer: AUD 392,400
## Explanation Let p denote the financial institution (FI) as the party making the calculation, and c denote the FI's counterparty. ### Step 1: Calculate Unilateral CVA (UCVA) The unilateral CVA from the perspective of the FI is: UCVA_p = - LGD_c × EPE_p × PD_c Where: - LGD_c = 1 - RR_c = 1 - 0.90 = 0.10 - EPE_p = AUD 48,000,000 - PD_c = 0.015 UCVA_p = -0.10 × 48,000,000 × 0.015 = AUD -72,000 ### Step 2: Calculate Bilateral CVA (BCVA) BCVA = CVA + DVA **CVA Calculation:** CVA_p = - LGD_c × EPE_p × PD_c × (1 - PD_p) CVA_p = -0.10 × 48,000,000 × 0.015 × (1 - 0.033) CVA_p = -0.10 × 48,000,000 × 0.015 × 0.967 = AUD -69,624 **DVA Calculation:** DVA_p = - LGD_p × ENE_c × PD_p × (1 - PD_c) Where: - LGD_p = 1 - RR_p = 1 - 0.75 = 0.25 - ENE_c = -48,000,000 (negative expected negative exposure) - PD_p = 0.033 - (1 - PD_c) = 0.985 DVA_p = -0.25 × (-48,000,000) × 0.033 × 0.985 DVA_p = 0.25 × 48,000,000 × 0.033 × 0.985 = AUD 390,060 **BCVA Calculation:** BCVA = CVA + DVA = -69,624 + 390,060 = AUD 320,436 ### Step 3: Calculate Change from UCVA to BCVA Change = BCVA - UCVA = 320,436 - (-72,000) = AUD 392,436 ≈ AUD 392,400 Therefore, the change in the charge when moving from UCVA to BCVA is approximately AUD 392,400.
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The manager of the CVA desk of a financial institution is reviewing the results of estimating a 1-year bilateral CVA (BCVA) associated with derivative exposure positions with a counterparty. The manager is concerned that the junior analyst who ran the analysis may have entered inputs to the CVA valuation model incorrectly, which led to the result being the unilateral CVA (UCVA) instead of the BCVA.
The manager reports that the discounted expected positive exposure of the financial institution to the counterparty is AUD 48 million for the coming year and is the same amount as the discounted expected positive exposure of the counterparty to the financial institution over the same period. Additional information on the two entities for the coming year is shown below:
| Financial Institution | Counterparty | |
|---|---|---|
| Annual probability of default | 3.3% | 1.5% |
| Expected recovery rate | 75% | 90% |
From the perspective of the financial institution, approximately what is the change in the charge if the analyst derives the BCVA instead of the UCVA?
A
AUD 141,600
B
AUD 320,400
C
AUD 390,100
D
AUD 392,400