Consider a three-period (t=0,1,2) binomial structure for a stock, with initial stock price =100. Over each of the next two periods, the price is expected to go up by 5% or down by 5%. Each period is three months. The risk-free interest rate is 4% per annum, with discrete compounding. The stock pays no dividend.

a) Taking the stock as underlying asset, what is the value of a 6-month European call option with strike price of $102?

b) Replicate the call option above, using the stock and the risk-free bond.

c) What is the value of an American put option with strike price $99?