We will derive a two$-$state call option value in this problem. Data: $S_0=$$$110$;$x=$$$120$;$1+r=1\mathrm{.}10.$ The two possibilities for $S_T$ are $$140$

and $$100.$ The portfolio consists of $2$ shares of stock and $4$ calls short.

Required:

a$.$ The range of $S$ is $$40$ while that of $C$ is $$20$ across the two states. What is the hedge ratio of the call? $($Round your answer to $2$

decimal places.$)$

Hedge ratio

b$.$ Calculate the value of a call option on the stock with an exercise price of $$120.($Do not use continuous compounding to calculate

the present value of $x$ in this example, because the interest rate is quoted as an effective per$-$period rate.$)($Do not round intermediate

calculations. Round your answer to $2$ decimal places.$)$

Call value