NO.PZ2024050101000096
问题如下：
Mary assigns to John a long position in an at-the-money (ATM) call option with a one year term and strike a 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 exposure (EE) 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)?
选项：
A.$6.15
B.$19.37
C.$24.32
D.$26.04
解释：
The BSM call option price = 100 × 0.64 - 100 × exp(-3%) × 0.40 = $25.182, which does not include counterparty risk incurred by the long option position (the short has no counterparty risk). The CVA-adjusted value = $25.182 - $23.00 × 5% × 75% = $24.32
题干中volatility of 60.0%没用到，什么时候会用到volatility这个条件呢？
