Question

Suppose that, for a particular three-year derivative entered into by a bank, two outcomes, A and B, are equally likely. Under outcome A, the values of the derivative at the midpoint of the first, second, and third years are 3, 5, and 7, respectively. Under outcome B, the values of the derivative at the midpoints of the first, second, and third years are $-2,-4$, and -6 . The probability of the counterparty defaulting each year is $1 \%$ and the probability of the bank defaulting each year is $0.5 \%$. Calculate the bank's CVA and DVA. Assume that interest rates are zero, no collateral is posted, and there are no other transactions between the two parties.

   Suppose that, for a particular three-year derivative entered into by a bank, two outcomes, A and B, are equally likely. Under outcome A, the values of the derivative at the midpoint of the first, second, and third years are 3, 5, and 7, respectively. Under outcome B, the values of the derivative at the midpoints of the first, second, and third years are $-2,-4$, and -6 . The probability of the counterparty defaulting each year is $1 \%$ and the probability of the bank defaulting each year is $0.5 \%$. Calculate the bank's CVA and DVA. Assume that interest rates are zero, no collateral is posted, and there are no other transactions between the two parties.
 
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Options, Futures, and Other Derivatives
Options, Futures, and Other Derivatives
John C. Hull 10th Edition
Chapter 9, Problem 14 ↓

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Step 1

The EE is the expected value of the derivative at each midpoint, weighted by the probability of each outcome. For outcome A: EE at midpoint of year 1 = 3 * 0.5% = 0.015 EE at midpoint of year 2 = 5 * 0.5% = 0.025 EE at midpoint of year 3 = 7 * 0.5% = 0.035 For  Show more…

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Suppose that, for a particular three-year derivative entered into by a bank, two outcomes, A and B, are equally likely. Under outcome A, the values of the derivative at the midpoint of the first, second, and third years are 3, 5, and 7, respectively. Under outcome B, the values of the derivative at the midpoints of the first, second, and third years are $-2,-4$, and -6 . The probability of the counterparty defaulting each year is $1 \%$ and the probability of the bank defaulting each year is $0.5 \%$. Calculate the bank's CVA and DVA. Assume that interest rates are zero, no collateral is posted, and there are no other transactions between the two parties.
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