Suppose today is 2nd August 2021, when the Afterpay share (APT.AX) is priced at $114.8. Consider an Afterpay option that expires on 18th November 2021, with a strike price of $120. Assume no dividends are paid on this stock. The annual historical standard deviation of Afterpay stocks is 51.27%. The risk-free rate is 0.153% with annual compounding. Ignore transaction costs (e.g. bid-ask spread).

a) Using a three-step binomial tree model, calculate theoretical prices today for a) a November American call option, b) a November American put option, c) a November European call option, and d) a November European put option on Afterpay. Draw the trees and show all calculation workings at each node.

b) Suppose that you observe that the market option price of European put on this stock is currently $4.5. Is there an arbitrage opportunity? If you see an arbitrage opportunity, present a strategy to earn riskless profit and construct a table showing the cashflows at initiation and expiration to demonstrate that your strategy is correct.