A stock is currently trading at $77.05. This stock is known to have a volatility of 0.30. Assume the risk-free rate is 5% per annum with continuous compounding for both lending and borrowing.

a)Draw a 2-step binomial tree for the next six months and label the future stock prices, Suu, Sud, Sdd, Su and Sd, where Suu stands for the stock price after two upticks, etc.

b) Consider an option which pays |ST 75| if the difference between ST and $75 is more than $12. Price this option with the 2-step binomial tree using the result of part (a).