$($Related to Checkpoint $20\mathrm{.}3)($Call option valuation$)$ Consider the following call option:

the current price of the stock on which the call option is written is $$19$;

the exercise or strike price of the call option is $$17$;

the maturity of the option is $90$ days or $0\mathrm{.}25$ year;

the $($annualized$)$ variance in the returns of the stock is $0\mathrm{.}14$ ; and

the risk$-$free rate of interest is $4\mathrm{.}1\%$ per annum.

a$.$ What is the value of this call option?

b$.$ Value the call option where the exercise price is $$24.$

c$.$ Value the call option under the original assumptions stated above but with an annualized variance in stock returns of $0\mathrm{.}31.$ Why did the value of the call option increase when compared to part a$?$

a$.$ The value of the call option with an exercise price of $$17$ is $ $($Round to the nearest cent.$)$

$($Answer A$,$B$,$ and C$)$