Problem $16-9($Algo$)$

We will derive a two$-$state call option value in this problem. Data: $s_{}=$$$150$;$x=$$$160$;$1+r=1\mathrm{.}10.$ The two possibilities for $s_T$ are $$180$ and $$100.$ The portfolio consists of $1$ share of stock and $4$ calls short.

Required:

o$.$ The range of $S$ is $$80$ while that of $C$ is $$20$ across the two states. What is the hedge ratio of the call? $($Round your answer to $2$ decimal places.$)$

Answer is complete and correct.

$\backslash$table$[[$Hedge ratio,$0\mathrm{.}25]]$

b$.$ Calculate the value of a calloption on the stock with an exercise price of $$160.($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.$)$

Answer is complete but not entirely correct.

$\backslash$table$[[$Call value,$5,250ox$