Explanation:
To calculate John's payment including CVA, we need to find the option premium and then subtract the CVA.
Using the Black-Scholes formula for call options:
Call = S × N(d₁) - K × e^(-rT) × N(d₂)
Where:
$100.00 (current stock price)$100.00 (strike price)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
CVA = EPE × PD × LGD
Where:
$23.00 (expected positive exposure)CVA = 23.00 × 0.05 × 0.75
CVA = 23.00 × 0.0375
CVA = $0.8625
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