(1) Let us assume that the stock price today is 80 and it is expected to either increase or decrease by 20% every period over the next three 6-months periods (three period Binomial tree). Also assume that the continuously compounded risk-free rate of interest is 3% per annum and the strike price is 87. [Total 33 marks] (a) Verify that the model is arbitrage free. [1 mark] (b) Calculate the price of an 18-month European Call option written on nondividend paying stock S [6 marks] and draw the binomial model [2 marks]. [8 marks] (c) Calculate the price of an 18-month European Put option written on nondividend paying stock S. [6 marks] (d) Verify if the put-call parity holds using the prices obtained in (b) and (c). [2 marks] (e) Calculate the price of an 18-month American Call option written on nondividend paying stock S [6 marks] and verify if an early exercise is optimal [2 marks]. [8 marks] (f) Calculate the price of an 18-month American Put option written on nondividend paying stock S [6 marks] and verify if an early exercise is optima