We will derive a two$-$state put option value in this problem. Data: $S_9=$$$110$;$x=$$$120$;$1+r=110.$ The two possibilities for $S_T$ are $$140$ and $$100.$

Required:

$0.$ The range of $S$ is $$40$ while that of $P$ is $$20$ across the two states. What is the hedge ratio of the put? $($Negotive value should be Indleated by o minus sign. Round your onswer to $2$ decimal ploces.$)$

Hedge ratio

b$.$ Form a portfolio of two shares of stock and four puts. What is the $($nonrandom$)$ payoff to this portfolio? $($Round your answer to $2$ decimal ploces.$)$

Nonrandom payoff

c$.$ What is the present value of the portfolio? $($Round your answer to $2$ decimal places.$)$

Present value

d$.$ Given that the stock currently is selling at $$110,$ calculate the put value. $($Do not round Intermedlote calculations and round your answer to $2$ decimal places.$)$

Put value