$1.\backslash ((17\backslash \%)\backslash )$ Robert would like to speculate on a possible decline in the stock price of HSY $($Hershey Company$).$ The current stock price of HSY is $\backslash (\backslash$$ $107\backslash ).$ Robert expects that in one year the stock price of HSY will be either $\backslash (\backslash$$ $125\backslash )($up move$)$ or $\backslash (\backslash$$ $85\backslash )($down move$).$ The exercise price of one$-$year European put option of HSY $\backslash (=\backslash$$ $105\backslash )$ and the one$-$period risk$-$free rate $\backslash ($ r$\_\{$f$\}=2\backslash \%\backslash )$ per annum $($NOT $\backslash ($ r$\_\{$c$\}\backslash )).$ Robert would like to construct a portfolio with the short sale of HSY shares and cash at hand to replicate the payoff of $1,000$ units of European put options of HSY$.($a$)(3\backslash \%)$ How many shares of HSY does Robert need to short sell now? $($b$)\backslash ((3\backslash \%)\backslash )$ How much $(\backslash$$$)$ does Robert need to save now? $($c$)(3\backslash \%)$ Calculate the percentage margin. $($Note: Percentage margin$=($equity$)/($short position$))($d$)(4\backslash \%)$ Calculate the current option premium of European put option of HSY $($per unit$)$ in the binomial setting. $($e$)(4\backslash \%)$ Calculate the current option premium of European call option of HSY $($per unit$)$ using put$-$call parity.