An analyst wants to use the Black-Scholes model to value call options on the stock of Heath Corporation based on the following data:
The price of the stock is $40.
The strike price of the option is $40.
The option matures in 3 months (t = 0.25).
The standard deviation of the stock's returns is 0.40, and the variance is 0.16.
σ The risk-free rate is 6%.
Given this information, the analyst then calculated the following necessary components of the Black-Scholes model:
σ d1 = 0.175
σ d2 = σ0.025
σ N(d1) = 0.56946
σ N(d2) = 0.49003
N(d1) and N(d2) represent areas under a standard normal distribution function. Using the Black-Scholes model, what is the value of the call optionσ

Question

An analyst wants to use the Black-Scholes model to value call options on the stock of Heath Corporation based on the following data:
 The price of the stock is $40.
 The strike price of the option is $40.
 The option matures in 3 months (t = 0.25).
 The standard deviation of the stock's returns is 0.40, and the variance is 0.16.
σ The risk-free rate is 6%.
Given this information, the analyst then calculated the following necessary components of the Black-Scholes model:
σ d1 = 0.175
σ d2 = σ0.025
σ N(d1) = 0.56946
σ N(d2) = 0.49003
N(d1) and N(d2) represent areas under a standard normal distribution function. Using the Black-Scholes model, what is the value of the call optionσ

Quizplus · Accepted Answer

$\begin{array}{ll}
\text { Stock price:} & \$ 40.00 \mathrm{~N}\left(\mathrm{~d}_{1}\right)=0.56940 \
\text { Strike price: } & \$ 40.00 \mathrm{~N}\left(\mathrm{~d}_{2}\right)=0.49003\
\text { Option maturity: } & 0.25 \
\text { Variance of stock returns: } & 0.16\
\text { Risk-free rate:  } & 6.0\% \
\end{array}$ 
The Black-Scholes model calculates the value of the call option as:
 $$\begin{aligned}
V & = p \left[ N \left( \mathrm {~d} _ { 1 } \right) \right] - \mathrm { Xe } - { } ^ { \mathrm { rt } } [ \mathrm { N } ( \mathrm { d } ) ] \
& = \$40 ( 0.56946 ) - \$40 \mathrm { e } - { } ^ { \mathrm { r } } (0 .49003 ) \
& = \$22.78- \$19.31 \
& = \$3.47
\end{aligned}$$

An Analyst Wants to Use the Black-Scholes Model to Value