i) Suppose that there are three European Call options with same maturity on the same underlying...

 

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i) Suppose that there are three European Call options with same maturity on the same underlying asset. The underlying asset will have a spot price of S7 at maturity. The call option prices are c, C2 & C3, and strike prices are x1, x2 & X3. Also, suppose that the strike prices have the following relationship: x1 < x2 < x3 and x3 - x2 = x2 - X1. Construct a portfolio with the three call options, and show that C2 0.5(c+ C3) (5 marks) Hint: the key to solve this problem is that you must construct a portfolio with the above three call options first, and do some scenario analysis (i.e. compare strike prices with the spot price and work out the portfolio value at maturity). The no-arbitrage pricing condition also applies. ii) Using the result in part (i) and put-call parity, show that P2 0.5(p1 + P3) In this case, P1, P2 & P3 are option prices for three European Put options with strike prices X1, X2 & X3. Note that x1, x2 & X3 follow the same relationship as given in the part (i) (3 marks) i) Suppose that there are three European Call options with same maturity on the same underlying asset. The underlying asset will have a spot price of S7 at maturity. The call option prices are c, C2 & C3, and strike prices are x1, x2 & X3. Also, suppose that the strike prices have the following relationship: x1 < x2 < x3 and x3 - x2 = x2 - X1. Construct a portfolio with the three call options, and show that C2 0.5(c+ C3) (5 marks) Hint: the key to solve this problem is that you must construct a portfolio with the above three call options first, and do some scenario analysis (i.e. compare strike prices with the spot price and work out the portfolio value at maturity). The no-arbitrage pricing condition also applies. ii) Using the result in part (i) and put-call parity, show that P2 0.5(p1 + P3) In this case, P1, P2 & P3 are option prices for three European Put options with strike prices X1, X2 & X3. Note that x1, x2 & X3 follow the same relationship as given in the part (i) (3 marks)