Use Black scholes model or software with at least all equations.

A stock trades now for $28 and pays continuous dividends proportional to its price at a rate of 0.02. The volatility of the stocks returns is 0.38 and r = .05. A super special put option expires in 2 years and will pay the excess of 25 over the stock price at that time. The payment is rounded up to the nearest 10 but is no less than 0.

a) What is the payoff if ST = 4?

b) What is the payoff if ST = 9?

c) What is the payoff if ST = 19?

d) What is the payoff if ST = 29? Define the piecewise payoff function. Graph the payoff.

e) Find the value of this super special put.