
Explanation:
To calculate the bilateral CVA (BCVA), we account for the probability of default of both counterparties and calculate both the CVA component (cost of counterparty default) and the DVA component (benefit from own default), assuming the default events are independent.
The CVA component for Prime Bank (expected loss if ABC Bank defaults and Prime Bank survives): CVA = \`$2`,500,000 \times (1 - 0.91) \times 0.023 \times (1 - 0.031) CVA = 2,500,000 \times 0.09 \times 0.023 \times 0.969 = \`$5`,014.58 \approx \`$5`,015
The DVA component for Prime Bank (expected gain if Prime Bank defaults and ABC Bank survives): DVA = \`$1`,800,000 \times (1 - 0.87) \times 0.031 \times (1 - 0.023) DVA = 1,800,000 \times 0.13 \times 0.031 \times 0.977 = \`$7`,087.16 \approx \`$7`,087
The net Bilateral CVA adjustment magnitude is the difference between the DVA and CVA components: BCVA = |DVA - CVA| = \`$7`,087 - \`$5`,015 = \`$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
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