Consider a European call option on a stock. The option has an exercise price of $$37,$ and the current price of the stock is $$34.$ The option expires in $12$ months. At expiration, the stock is expected to be either $$30$ or $$45.$ The risk$-$free rate is $3\%.$

a$.$ Using the replicating portfolio approach, what is the price of this option?

b$.$ If the prices of the stock at expiration were expected to be $$33$ or $$41($instead of $$30$ or $$45),$ would the price of the option be higher, lower, or the same? No calculations are necessary, but be sure to explain your reasoning. $($No credit will be given if no clear reason is provided$)$

c$.$ If the option expired in $6$ months instead of $12$ months, would the price of the option be higher, lower, or the same? No calculations are necessary, but be sure to explain your reasoning. $($No credit will be given if no clear reason is provided$)$