Assume all options are European, and that the underlying asset is a non-dividend paying stock, unless otherwise specified.

(a) A protective put strategy involves buying both a put option on a stock and the underlying stock itself.

i. Draw a payoff diagram (not a profit-and-loss diagram) for a protective put strategy. Make sure to label all relevant parts of the diagram. Why do you think this strategy has its name? (5 marks)

ii. Using put-call parity, explain why the payoff of a protective put resembles the shape of the payoff of a call option. (5 marks)

(b) You observe two call options, A and B, with the same exercise price, written on the same underlying asset. Option A matures in one year, while B matures in 18 months. Which option has the higher value? Explain. (5 marks)

(c) The value of a European put option must satisfy the following restriction: p₀ ^-rT ₀ where P₀ is the current put price, ₀ is the current price of the underlying stock, is the exercise price, > 0 is the annualised continuously compounded risk-free rate, and is the time till expiration. Prove by contradiction that the above arbitrage restriction must hold, i.e. show that if the condition does not hold, there is an arbitrage opportunity. (4 marks)