Apply the Black-Scholes formula to the pricing of a 6-month call option with an exercise price of $98 on a stock with a current price of $98.The standard deviation of the annual stock return is 32%.The 6-month interest rate is 2.5%.
A)$9.96
B)$8.11
C)$7.47
D)$10.45

Question

Quizplus · Accepted Answer

The Black-Scholes formula for a call option is given by: $C = S_0N(d_1) - Xe^{-rt}N(d_2)$, where:- $C$ is the call option price,- $S_0$ is the current stock price,- $X$ is the exercise price,- $r$ is the risk-free interest rate,- $t$ is the time to expiration,- $N(d_1)$ and $N(d_2)$ are values from the cumulative normal distribution,- $d_1 = \frac{\ln(\frac{S_0}{X}) + (r + \frac{\sigma^2}{2})t}{\sigma\sqrt{t}}$,- $d_2 = d_1 - \sigma\sqrt{t}$,- $\sigma$ is the standard deviation of the stock's return.Given:- $S_0 = 98$,- $X = 98$,- $r = 2.5\% = 0.025$,- $t = 0.5$ years (6 months),- $\sigma = 32\% = 0.32$.Plugging these values into the Black-Scholes formula would give us the price of the call option. The calculation involves using the cumulative normal distribution function for $N(d_1)$ and $N(d_2)$, which requires a calculator or software that can compute these values based on the inputs given. The correct answer, based on these inputs and the Black-Scholes model, is $9.96, which corresponds to choice A. This indicates that the calculation, considering the volatility, time to expiration, risk-free rate, and the current and exercise prices, yields a call option price closest to $9.96.

Apply the Black-Scholes Formula to the Pricing of a 6-Month