Consider a three-period binomial model with three years expiration time, the stock price is $200, continuously compounded risk-free rate is 5%, continuously compounded dividend yield rate is 3% and the volatility is 30%.

(a) What is the price of a European call option with a strike of $190?

(b) What is the price of a European put option with a strike of $190?

(c) Calculate the price of an American call option with a strike of $190.

(d) If the stock price is $190, and the continuously compounded risk-free rate and continuously compounded dividend yield rate are changed to 3% and 5% respectively, with other values remaining unchanged, explain and demonstrate how you can find the price of a European call option with a strike of $200 without calculation.