Alex would like to speculate on a possible rise in the stock price of FB $($Facebook$).$

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 call $($put$)$

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

like to construct a portfolio with the stock and cash from borrowing to replicate the payoff of

$200$ units $(2$ contracts$)$ of European call options of FB$.$

$($a$)(3\%)$ How many shares of FB does Alex need to buy now?

$($b$)(3\%)$ How much $($$$)$ does Alex need borrow now?

$($c$)(3\%)$ Calculate the percentage margin $($Note: percentage margin$=($equity$)/($value of stock$)).$

$($d$)(4\%)$ Calculate the current price of European call option of FB $($per unit$)$ in the binomial

setting.

$($e$)(4\%)$ Calculate the current price of European put option of FB $($per unit$).$