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Answer: $24.32
## Explanation To calculate John's payment including CVA, we need to find the option premium and then subtract the CVA. ### Step 1: Calculate the Black-Scholes option premium Using the Black-Scholes formula for call options: Call = S × N(d₁) - K × e^(-rT) × N(d₂) Where: - S = $100.00 (current stock price) - K = $100.00 (strike price) - r = 3.0% (risk-free rate) - T = 1 year - N(d₁) = 0.64 - N(d₂) = 0.40 Call = 100 × 0.64 - 100 × e^(-0.03×1) × 0.40 Call = 64 - 100 × 0.9704 × 0.40 Call = 64 - 38.82 Call = $25.18 ### Step 2: Calculate CVA CVA = EPE × PD × LGD Where: - EPE = $23.00 (expected positive exposure) - PD = 5.0% (probability of default) - LGD = 75.0% (loss given default) CVA = 23.00 × 0.05 × 0.75 CVA = 23.00 × 0.0375 CVA = $0.8625 ### Step 3: Calculate John's payment including CVA John has a long position, so he pays the premium but receives credit for the counterparty risk: Payment = Option Premium - CVA Payment = 25.18 - 0.8625 Payment = $24.3175 ≈ $24.32 Therefore, the nearest amount to John's payment including CVA is **$24.32**, which corresponds to option C.
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Mary assigns to John a long position in an at-the-money (ATM) call option with a one-year term and a strike price of $100.00. The current stock price is $100.00 with volatility of 60.0%. The risk-free rate is 3.0% with continuous compounding. N(d₁) = 0.64 and N(d₂) = 0.40. The present-valued expected positive exposure (EPE) to the counterparty, who holds the short option position, is $23.00 with a probability of counterparty default of 5.0% and loss given default (LGD) of 75.0%.
Which is nearest to John's payment for the long option position, if his cost includes a credit valuation adjustment (CVA)?
A
$6.15
B
$19.37
C
$24.32
D
$26.04
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