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Explanation:
Bilateral CVA incorporates both the Credit Value Adjustment (CVA) and the Debt Value Adjustment (DVA), factoring in the joint probability of default. First, find the individual CVA and DVA components considering the probability that one party defaults while the other survives.
Loss Given Default (LGD):
$1 - 87% = 13%$$1 - 91% = 9%$Prime Bank's CVA (incorporating ABC's default and Prime's survival): \text{CVA} \approx 0.09 \times 0.023 \times 0.969 \times 2,500,000 \approx \`$5`,014.58 \approx \`$5`,015
Prime Bank's DVA (incorporating Prime's default and ABC's survival): \text{DVA} \approx 0.13 \times 0.031 \times 0.977 \times 1,800,000 \approx \`$7`,087.16 \approx \`$7`,087
Bilateral CVA (net adjustment magnitude): \text{BCVA} = |\text{CVA} - \text{DVA}| = |5,015 - 7,087| = \`$2`,072
Thus, the absolute net bilateral CVA adjustment is `$2`,072.
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Q.77 Assume that ABC Bank and Prime Bank are counterparties to each other and Prime Bank's discounted expected positive exposure to ABC Bank is $2,500,000, and its discounted expected negative exposure to ABC Bank is $1,800,000. Additionally,
| Parameter | Prime Bank | ABC Bank |
|---|---|---|
| Annual probability of default | 3.1% | 2.3% |
| Recovery rate | 87% | 91% |
What is Prime Bank's bilateral CVA?
A
$5,015
B
$7,087
C
$2,072
D
$9,777