Consider a European put option on a stock that does not pay dividends. The current price for the share (0) is 200 and the option has an exercise price ("strike") equal to 190. The risk-free interest rate is 6% p.a. continuously and the share has a volatility equal to 30%. Time to lapse is six months Suppose then that the underlying pays a dividend equal to 10 after 1.5 months and also after 4.5 months. Otherwise the information as at the beginning of the assignment.

a) Find the values of the European type of call option when considering the dividend payments.

b) Find the value of the corresponding European-type put option.

c) Then assume that the options are of the American type. Find using Blacks approach the value of an American-type call option when considering dividend payments.