$(10\%$; $2\%$ for each subquestion$)$ 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$(r_c)=1\mathrm{.}02),T=2$ 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$)$ Calculate $f(x)=SN(d_1)-x{e}^{-rT}N(d_2)-p$ using the initial selected exercise price $x$ of $40\mathrm{.}84.$

$($c$)$ Calculate $f^{\text{'}}(x)=-e^{-rT}N(d_2)$ using the initial selected exercise price $x$ of $40\mathrm{.}84.$

$($d$)$ Based on $x_{n+1}=x_n-\frac{f(x_n)}{f^{\text{'}}(x_n)},$ 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.