6. A firms stock sells at $50. There are no dividend payouts for the next three months. The risk-free rate is 4% per annum. The volatility is estimated at 30% a year. Assume the stock price is lognormally distributed.

a) What price should a 3-month European call option with a strike price of $55 sell for?

b) What price should a 3-month European put option with a strike price of $55 sell for?

c) What will your answers to a) and b) change if there are ex-dividend dates in one month and two months, and the dividend on each ex-dividend date is expected to be $1?

d) What will your answers to a) and b) change if the stock pays continuous dividends with a dividend yield rate of 2% per year?