Suppose the price of Apple stock is 20 dollars today. Each month, Apple has a 50% chance of going up 3% and a 50% chance of going down 2%. The monthly risk free rate is 0.2% and remains constant over time.

(a) What is the fair market price for a one month put option of Apple with strike price 20? (b) Consider a call option with a strike price of 20 of maturity 2 months written on Apple stock. After one month, what is the value of this option if Apple initially goes up 3%? What if it initially goes down 2%? (c) What is the initial fair market value of this 2 month option?