The following information is given for the stock of Akamai

Technologies $($AKAM$).$ S$=39\mathrm{.}25,$ annual volatility$=45\%,$ effective annual interest rate $=2\mathrm{.}0\%($i$.$e$.,$

exp$($rc$)=1\mathrm{.}02),$ T$=2$ years, and no cash dividend is expected by option expiration $($for analytical

simplification$).$ In a $$zero$-$cost collar$$ contract often used by executives trying to lock in gains or hedge

insider holding, Don sells European call options, if called upon, to sell shares at $A $($higher$).$ And he can

use the proceeds to buy European put options, giving him the right to sell shares at $B $($lower$).$ This

arrangement covers Don$$s $100,000$ AKAM shares and is exercisable $2$ years from now.

$($a$)$ If Don sets the value of B at $25,$ calculate the value of put option $($p in part $($b$))$ for each share hedged.

$($b$)$ CalculatepdNXedSNXf rT $=)()()(21$ using the initial selected exercise price X of $40\mathrm{.}84.$

$($c$)$ Calculate$)()(2$

$\text{'}$ dNeXf rT$$

$=$ using the initial selected exercise price X of $40\mathrm{.}84.$

$($d$)$ Based on$)($

$)($

$\text{'}1$

n

n

nn xf

xf

xx $=+,$ what is our new guess for the implied exercise price?

$($e$)$ Find the exercise price of A for the call option contained in the zero$-$cost collar contract.