A stock currently trades at $52. It is expected that dividends of $1.00/share will be paid to owners of the stock at 1 month and at 4 months from the current date. Consider these dates as ex-dividend dates as well. The continuously compounded risk free rate is 5%. European call and put options on the stock with exercise prices of $50 and 6 months to the expiration date are currently trading.

a) Calculate the lower bound for the value of the European call. (1 mark)

b) How would you arbitrage if the European call option has a market price (premium) of $1.00? In your answer clearly identify your position in each relevant instrument. (1 mark)

c) If the European call option has a market price (premium) of $2.00, based on put-call parity, what should be the price of a European put on the stock with the same exercise price and time to expiration? (1 mark)

d) Calculate the lower bound for the value of an American call option on the stock with an exercise price of $50 and a time to expiration of 6 months. (1 mark)