We will derive a two$-$state put option value in this problem. Data:$$S$0$S$0=$ $$100$;$$X$=$ $$110$; $1+$r$=1\mathrm{.}10.$ The two possibilities for$$STST$$are $$130$ and $$80.$

Required:

a$.$ The range of$$S$$is $$50$ while that of$$P$$is $$30$ across the two states. What is the hedge ratio of the put?

Note: Negative value should be indicated by a minus sign. Round your answer to $2$ decimal places.

b$.$ Form a portfolio of three shares of stock and five puts. What is the $($nonrandom$)$ payoff to this portfolio?

Note: Round your answer to $2$ decimal places.

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

Note: Round your answer to $2$ decimal places.

d$.$ Given that the stock currently is selling at $$100,$ calculate the put value.

Note: Do not round intermediate calculations and round your answer to $2$ decimal places.