We will derive a two$-$state put option value in this problem. Data: S$0=$

$90$; X $=100$; $1+$ r $=1\mathrm{.}10.$ The two possibilities for ST are $130$ and $70.$

a$.$ What is the hedge ratio of the put?

b$.$ What is the $($nonrandom$)$ payoff to a riskless portfolio constructed by

this stock and put option?

c$.$ What is the present value of the portfolio?

d$.$ Given that the stock currently is selling at $90,$ what is the value of the

put option?