Problem $1.$ Consider two American Call Options. One of them is written on a

dividend paying stock and one on a non$$dividend paying stock. To price these

options, you need to use either the Black$$Scholes formula or the multiplicative

binomial tree approximation or both. For each of the following statements

indicate if they are correct or false. Justify your answer.

$($a$)$ Black$-$Scholes method for the one written on a non$-$dividend paying stock.

$($b$)$ Black$-$Scholes method for the one written on a dividend paying stock:

$($c$)$ Binomial tree method for the one written on a non$-$dividend paying stock:

$($d$)$ Binomial tree method for the one written on a non$-$dividend paying stock:

Two points are awarded for indicating correctly true$/$false and three points for

correct explanation.