16. Derivatives [10 marks] a) Suppose that there exist futures contracts as well as European call options and put options for a non-dividend paying stock. All contracts expire in one year. The futures price is Fo, and the strike price of both the call and the put is X. Use parity conditions to show that if there is no arbitrage and Fo = X, then the call price equals the put price. [5 marks) b) The relationship in part (b) only holds if the options are European. How does the relationship between the call price and the put price change if the options are American? (Hint: Consider the value of exercising an American option early.) (5 marks] 16. Derivatives [10 marks] a) Suppose that there exist futures contracts as well as European call options and put options for a non-dividend paying stock. All contracts expire in one year. The futures price is Fo, and the strike price of both the call and the put is X. Use parity conditions to show that if there is no arbitrage and Fo = X, then the call price equals the put price. [5 marks) b) The relationship in part (b) only holds if the options are European. How does the relationship between the call price and the put price change if the options are American? (Hint: Consider the value of exercising an American option early.) (5 marks]