Which of the following option is false? Select the most suitable answer.

a. For American options without dividend payment, the difference between call and put prices should be lower than or equal to the difference between stock price and the present value of the strike price.

b. The intrinsic value of an option may equal the option premium.

c. For American options, put-call parity provides an upper and a lower bound for the difference between call and put prices.

d. The European put price plus the stock price must equal the European call price plus the present value of the strike price and the present value of the dividend (if there is a dividend payment).

e. Call option writer has limited profit, while put option writer has an unlimited profit.