A European call option and put option on a stock both have a strike price of $40 and an expiration date in 3 months. The call sells for $4 and the put sells for $3.5. The risk-free rate is 10% per annum for all maturities, and the current stock price is $41. 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]