Question 3 (13 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 at maturity. The call option prices are 1, 2 & 3, and strike prices are 1, 2 & 3. Also, suppose that the strike prices have the following relationship: 1 < 2 < 3 and 3 2 = 2 1. Construct a portfoliowith the three call options, and show that 2 0.5(1 + 3)

Hint: the key to solve this problem is that you must construct a portfolio with the above three call options, 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 2 0.5(1 + 3)

In this case, 1, 2 & 3 are option prices for three European Put options with strike prices 1, 2 & 3. Note that 1, 2 & 3 follow the same relationship as given in the part (i)