A stock is currently selling for $100. The stock price could go up by 4.2% or fall by 4% each month. The monthly risk-free interest rate is 0.3%. We want to calculate the price of a put option on the stock with an exercise price of $100 and a maturity of two months by using the two-stage binomial method. To that end (a.) Calculate the risk neutral probability that the stock will go up. [if, and only if, you cannot find the probability in (a.), use 0.45 for the next two parts ] (b.) Find the price of the option mentioned above if it is European. (c.) Find the price if it is an American option