Please provide your work for questions $1$ and $2.$

$1.$ Create a European Call Option with eight movements and give me the price.

The inputs are

Spot$=10$

Strike$=12$

R$=8\%$

Delta P$=2$

Periods$=8$

P$($u$)=\mathrm{.}6$

P$($d$)=\mathrm{.}4$

$2.$ Create an American Call Option with eight movements and give me the price.

The inputs are

Spot$=10$

Strike$=12$

R$=8\%$

Delta P$=2$

Periods$=8$

P$($u$)=\mathrm{.}6$

P$($d$)=\mathrm{.}4$

$3.$ Randomly change the inputs and tell me how the price changes and if it is an expected direction $($on both European and American$)$

$4.4.$ How would the answers to number three change if we did a put option instead of a call option?

$5.5.$ Would we expect the changes to be higher for an American or European option?