Consider a stock which is currently selling for $50. Construct a two-step binomial tree, 1-month and 2-months respectively for each of the two steps. The stock market volatility is 30%, the rate of interest is assumed to be 5% and the exercise price is $52.

(i) Calculate the price of an American Put.

(ii) Provide a graphical illustration to demonstrate how the put price and the put payoff change with respect to changes in the stock price.

(iii) Put all in an excel format