Suppose that Auckland International Airport (NZX:AIA) currently trades at $7.69. The interest rate is 2.5% (with continuous compounding), and AIA shares have a volatility of 32%. Set up a two step binomial tree for the stock, with each step representing six months. Assume that AIA will pay no dividends over the next year. (a) What is the value of a European put option with strike price $7.74, maturing in one year's time? 5 marks (b) What is the value of an American put option with strike price $7.74 maturing in one year's time? 5 marks (c) Use the American put-call parity relationship and your answer to part 4b to place bounds on the value of a one year American call option written on the AIA with strike $7.74.5 marks (d) Now price a one year American call option with strike $7.74, and verify that it satisfies your bound from part 4 c. 5 marks Suppose that Auckland International Airport (NZX:AIA) currently trades at $7.69. The interest rate is 2.5% (with continuous compounding), and AIA shares have a volatility of 32%. Set up a two step binomial tree for the stock, with each step representing six months. Assume that AIA will pay no dividends over the next year. (a) What is the value of a European put option with strike price $7.74, maturing in one year's time? 5 marks (b) What is the value of an American put option with strike price $7.74 maturing in one year's time? 5 marks (c) Use the American put-call parity relationship and your answer to part 4b to place bounds on the value of a one year American call option written on the AIA with strike $7.74.5 marks (d) Now price a one year American call option with strike $7.74, and verify that it satisfies your bound from part 4 c. 5 marks