Consider an economy which is to go into a booming development or enter a recession in the near future. You are interested in buying a European call option written on a firms non-dividend-paying common stock, with a strike price of $84 and six months until expiration. Currently, the firms stock price is $80 per share. In six months, you expect this stock to be trading at either $96 per share or $72 per share, depending on whether the economy booms or falls into recession respectively.

1. 1.1. If you are able to borrow and lend at the risk-free EAR of 5 percent, how can you create a portfolio today that will exhibit no risk in 6 months? [2 points]

2. 1.2. What should be the fair value of the call options price today? [2 points]

3. 1.3. If presently the market is not offering the call options that you want to buy (described in the problem), is there a way to create a synthetic call option with identical payoffs to the call option described above? If there is, how should one do it? If not, explain why. [2 points]

4. 1.4. How much would it cost to create the synthetic call option cost, if possible? Is this greater than, less than, or equal to what the actual call option costs? Does this make sense? Explain. [2 points]