Pick two stocks, one more volatile and one less so.

Construct a two-period binomial tree for each stock.

Based on the binomial trees in step 2, price (a) a European at-the-money put option and (b) an American at-the-money put option for each stock. You can choose any time to maturity (T), e.g., 1 month, 3 months, or 1 year. The strike price can be the stock close price on the day you start your assignment. There are in total 4 options you need to price.