Consider a market in which currently two assets are traded: (1) A stock, currently selling for $40, which is expected to increase in value by 40% or decrease in value by 20% every year. (2) A zero-coupon risk-free bond with one year maturity that costs $100 and offers 2% annually compounded interest. Suppose the financial institutions are considering the sale of the third asset with maturity of one year whose value at maturity equals max(S-40, 0)? S is the value of the stock at the time the asset matures and max(x, y) equals the greater of the two values x and y.
a) What should be the fair price of this asset today?
b) Suppose the price of this asset today equals $4. Is there anything you could do to make arbitrage money? Show formally the arbitrage strategy.