An ABCspread is a combination of option positions that involves four strike prices (see figure below, which shows the gross payoffs). For this problem, assume that the options are European with the same maturity and thata >0.

1. Find the option positions and strike prices necessary to obtain the ABC spread. Show that your portfolio replicates the spread payoffand assume that the underlying options are allcalloptions.
2. Find the option positions and strike prices necessary to obtain the ABC spread. Show that your portfolio replicates the spread payoffand assume that the underlying options are allputoptions.
3. Consider the following strategy: (i) buy a call with a strike price of ABC, and (ii) buy a put with a strike price of X+3a. Assuming no arbitrage, show mathematically that the initial investment (i.e. the amount of money you need to pay att= 0) to create the strategy is higher than the initial investment to create the ABC spread.