A European call option and put option on a stock both have a strike price of $21 and an expiration date in 4 months. The call sells for $2 and the put sells for $1.5. The risk-free rate is 10% per annum for all maturities, and the current stock price is $20. The next dividend is expected in 6 months with the value of $1 per share.

(a) describe the meaning of put-call parity. [2 marks]

(b) Check whether the put-call parity holds. [2 marks]

(c) If the put-call parity does not hold, describe step-by-step how an investor can take the advantage of this arbitrage opportunity to make a profit. [7 marks]

(d) If these two options are American options rather than European options, briefly explain whether the put-call parity still holds here. [2 marks]