You've just been introduced to the$$ Black$-$Scholes option pricing model and want to give it a$$ try, and would like to use it to calculate the value of a call option on TriHawk stock. $$ Currently, TriHawk's common stock is selling for

$ $25$$$25$

per$$ share, and the call option you are considering has an exercise or strike price of

$ $20$$$20$

with a maturity of $90$ days or

$0\mathrm{.}250\mathrm{.}25$

year. In$$ addition, you have calculated the$($annualized$)$ variance in its stock returns to be

$0\mathrm{.}090\mathrm{.}09.$

If the annual$$ risk$-$free rate of interest is

$4\mathrm{.}04\mathrm{.}0$

$$percent$,$ what would the value of this call option$$ be$?$ How would your answer change if there was only one month left to$$ expiration, but everything else remained the$$ same? $$ Now, what would happen to the value of this call option if the annualized variance in stock returns was

$0\mathrm{.}150\mathrm{.}15$

rather than

$0\mathrm{.}090\mathrm{.}09?$

Question content area bottom

Part $1$

a$.$The value of the call option with an exercise price of

$ $20$$$20$

is

$$$enter your response here.

$($Round to the nearest$$ cent.$)$

Part $2$

b$.$The value of the call option with one month left to$$ expiration, but everything else remaining the same is

$$$enter your response here.

$($Round to the nearest$$ cent.$)$

Part $3$

c$.$Using the original assumptions from$$ above, the value of the call option with a variance of

$0\mathrm{.}150\mathrm{.}15$

is

$$$enter your response here.

$($Round to the nearest$$ cent.$)$

Part $4$

Why did the value of the call option increase when compared to part a$$ above?$($Select the best choice$$ below.$)$

A$.$

When volatility$$ increases, the potential to make money on the option is greater because the risk is less. For this$$ reason, investors are willing to pay more for options on more volatile stocks.

B$.$

When volatility$$ increases, the potential to make money on the option is greater because there is an increase in the upside$$ potential; however, you can still lose no more than the price of the option. For this$$ reason, investors are willing to pay more for options on more volatile stocks.

C$.$

When volatility$$ increases, the potential to make money on the option is less because the risk is greater. For this$$ reason, investors are willing to pay more for options on more volatile stocks.

D$.$

When volatility$$ decreases, the potential to make money on the option is less because the risk is greater. For this$$ reason, investors are willing to pay more for options on more volatile stocks.

The value of the call option with an exercise price of @CURR$\{20\}$ is $$($Round to the nearest cent.$)$The value of the call option with one month left to expiration, but everything else remaining the same is $$($Round to the nearest cent.$)$Using the original assumptions from above, the value of the call option with a variance of $0\mathrm{.}15$ is $$($Round to the nearest cent.$))$