Q3.

a) Use the Black (1975) approximation to calculate the price of an American call option with a dividend given the following information:

- Price of the underlying stock: $49

- Option strike price: $44

- Risk-free interest rate: 2.77%

- Volatility (variance) of the return on the share: 22%

- Two dividend dates - in two months: D1 = 0.82

- in five months: D2 = 0.82

- This option fails in six months

b) Is it possible to use the model in a) to calculate the price of a put? Define and explain an alternative if not.