Chicago investment firm is offering a new financial derivative called a “windy put”. The windy put is European and has a payoff at expiration equal to Max(0.75S T , 70-S T ), where S T is the price of the underlying stock on the expiration date.

a. Graph the payoff of the windy put on the expiration date as a function of the underlying stock on that date.

b. Decompose (break down) a windy put into a portfolio of underlying stocks and standard European put options on the underlying stock.

c. Using your answer to b. above, price a windy put by two methods: The Black Scholes Merton model and a three-step binomial tree. Use the following data:

- Underlying stock price is $50 today

- Time to expiration is 1 year

- Risk-free rate is 6%

- Standard deviation of the underlying stock return is 20%