Question: (b) (i) Suppose two put options with the same maturity on the same underlying are available. The first option has an exercise price of 45

(b) (i) Suppose two put options with the same maturity on the same underlying are available. The first option has an exercise price of 45 and trades for 4 and the second option has an exercise price of 40 and trades for 2. Plot payoff and profit of the following strategy: write a put with X = 40 and buy a put with X = 45. Does a positive or a negative cash-flow occur when forming this portfolio? [5 marks]

(ii) The price of a European call that expires in 9 months and has a strike price of 50 is 4. The underlying stock price is 48. The continuously compounded risk-free rate is 8% p.a. What is the price of a European put option that expires in 9 months and has a strike price of 50? Then explain carefully the arbitrage opportunities in this case if the European put price is 6. [5 marks]

(c) Explain with an arbitrage argument why an American call option on a non-dividend paying share will never be exercised before expiration date. What are the implications of this result for the pricing of the American call option?

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