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 $86 and six months until expiration. Currently, the firms stock price is $90 per share. In six months, you expect this stock to be trading at either $99 per share or $72 per share, depending on whether the economy booms or falls into recession respectively. There is also a risk-free pure discount bond which matures in 6 months. This bond is currently selling for $961.5385.

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 firm's non-dividend-paying common stock, with a strike price of $86 and six months until expiration. Currently, the firm's stock price is $90 per share. In six months, you expect this stock to be trading at either $99 per share or $72 per share, depending on whether the economy booms or falls into recession respectively. There is also a risk-free pure discount bond which matures in 6 months. This bond is currently selling for $961.5385. 1.1. How can you create a portfolio today that will exhibit no risk in 6 months? [2 points] 1.2. What should be the fair value of the call option's price today? [ 2 points] 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] 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] 1.5. Assume that Achraf Hakimi observes that a European put option written on ABC, Inc. with a strike price of $86 and six months until expiration is currently selling for $3.6923. Is there a way for him to make riskless profit? If there is, how should he do it? [2.4 points] 1.6. Assume, in the same economy, the market is offering a non-divisible investment project which generates $210K, of cash flows, if the economy booms or $70K if otherwise in six months. How much should investors in the market be willing to invest in this project? [ 3 points]