$(17\%)$ In the one$-$period binomial model, the stock price of United Parcel Service $($UPS$)$ is $$135\mathrm{.}6$ in the up move and $$90\mathrm{.}4$ in the down move. Also, the one$-$period risk$-$free interest rate $r_f=0\mathrm{.}25\%(NOT{r}_c).$ UPS' current stock price $S=$$$113,$ UPS' $110$ European put option price is $P($unknown$).$

$($a$)(4\%)$ Calculate the risk neutral probability in the up move.

$($b$)(4\%)$ If you buy $1,000$ units $(10$ contracts$)$ of the European put option, how many shares $(2$ decimal places$)$ of the stock do you buy to form a risk free $($hedge$)$ portfolio $(hS+1,000P?$

$($c$)(4\%)$ What is the present value $(2$ decimal places$)$ of your hedge portfolio $(hS+1,000P?$

$($d$)(5\%)$ Find the current price $P(2$ decimal places$)$ of the European put option based on the one$-$period binomial model.