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?