Using the information in Table 15.5, assume that the volatility of oil is 15%.
a. Show that a bond that pays one barrel of oil in 1 year sells today for $19.2454.
b. Consider a bond that in 1 year has the payoff S1 + max(0, K1 − S1) − max(0, S1− K2). Find the strike prices K1 and K2 such that K2 − K1= $2, and the price of the bond is $19.2454. How would you describe this payoff?
c. Now consider a claim that in 1 year pays S1− $20.50 + max(0, K1− S1) − max(0, S1 − K2), where K1 and K2 are from the previous answer. What is the value of this claim? What have you constructed?