i)Suppose that there are threeEuropean Calloptions with same maturity on the same underlying asset. The underlying asset will have a spot price ofat maturity. The call option prices are1, 2& 3,and strike prices are1, 2& 3. Also, suppose that the strike prices have the following relationship:1< 2< 3and3 2= 2 1. Construct aportfoliowith 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 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) andput-call parity, show that2 0.5(1+ 3)

In this case,1, 2& 3are option prices for threeEuropean Putoptions with strike prices1, 2& 3. Note that1, 2& 3follow the same relationship as given in the part (i)