Suppose the current stock price is $$41,$ the standard deviation of the $log$ annual return is $0\mathrm{.}3,$ the continuously compounded interest rate is $8\%$ and dividend yield is $1\%.$

Use excel for the following calculation and paste the binomial trees.

If we divide one year into ten periods and model the stock price movement as binomial for each period, what's the evolution path of the stock price?

Consider a European call and put option with strike price of $$40.$ What is their premium, respectively? Check if put$-$call parity holds.

Consider an American call and put option with strike price of $$40.$ What is their premium, respective? Is there ever early exercise? Does put$-$call parity hold?