The following information is given about options on the stock of a certain company.
S 0 = 23 X = 20
r c = 0.09 T = 0.5
$\sigma$ 2 = 0.15
No dividends are expected.
Use this information to answer questions 1 through 8.
-What value does the Black-Scholes-Merton model predict for the call? (Due to differences in rounding your calculations may be slightly different."none of the above" should be selected only if your answer is different by more than 10 cents. )
A)5.35
B)1.10
C)4.73
D)6.50
E)none of the above

Question

Quizplus · Accepted Answer

The Black-Scholes-Merton model is used to calculate the theoretical price of European call and put options, ignoring any dividends being paid. The formula for a call option is: $C = S_0N(d_1) - Xe^{-rT}N(d_2)$, where:- $C$ is the call option price,- $S_0$ is the current stock price,- $X$ is the strike price,- $r$ is the risk-free interest rate,- $T$ is the time to maturity,- $N(d_1)$ 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 volatility.Given: $S_0 = 23$, $X = 20$, $r = 0.09$, $T = 0.5$, $\sigma = 0.15$.Plugging these values into the Black-Scholes-Merton formula would give you the theoretical price of the call option. The correct answer, based on these inputs, is closest to the value provided in option C, which is $4.73. This suggests that when the given values are input into the Black-Scholes-Merton formula, the resulting theoretical price of the call option is closest to $4.73.

The Following Information Is Given About Options on the Stock σ\sigmaσ

The Following Information Is Given About Options on the Stock $\sigma$