Problem $16-9($Algo$)$

We will derive a two$-$state call option value in this problem. Data: $s_0=$$$210$;$x=$$$220$;$1+r=1\mathrm{.}10.$ The two possibilities for $s_T$ are $$250$

and $$130.$ The portfolio consists of $1$ share of stock and $4$ calls short.

Required:

a$.$ The range of $S$ is $$120$ while that of $C$ is $$30$ across the two states. What is the hedge ratio of the call? $($Round your answer to $2$

decimal places.$)$

Answer is complete and correct.

Hedge ratio

$0\mathrm{.}25$

b$.$ Calculate the value of a call option on the stock with an exercise price of $$220.($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.