The current stock price of FB is $$29.$ Alex expects that in one year the stock price of

FB will be either $$40($up move$)$ or $$20($down move$).$ The exercise price of one$-$year European

put option of FB$=$$$30$ and the one$-$period risk$-$free rate rf $=2\%$ per annum $($NOT rc$).$ Also,

investors can freely trade $($either buy or short sell$)$ the GS fund, $\{200$ units of FB European put

option $+200$ shares of FB stock$\},$ and the MS fund, $\{$N shares of FB stock $+$ risk$-$free one$-$year

CD with original investment $B$\}$ in the market. That is$,$ no arbitrage opportunity exists.

$($a$)(3\%$; $3\%)$ Find the gross payoffs $($$$)$ of the GS fund in the up and down move, respectively.

$($b$)(3\%$; $3\%)$ The GS fund and MS fund have the same future payoffs in one year. Find the

values of N and B$.$

$($c$)(3\%)$ Calculate the current price $($$$)$ of European put option of FB $($per unit$).$

$($d$)(2\%)$ If the GS fund is perfectly equivalent to the MS fund, then we can see $\{200$ units of

FB European put option$\}=\{$short sell Y shares of FB stocks $+$ cash $C$\}.$ Use this idea to

calculate the equivalent percentage margin $(\%)$ for $200$ units of FB European put option.

$($Note: Percentage margin$=($equity$)/($short position$)).$

Answer rating: 100% (QA)

a To find the gross payoffs of the GS fund in the up and down moves we need to consider the different scenarios In the up move The stock price of FB i... View the full answer