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 ˆ’ S1) ˆ’ max(0, S1ˆ’ K2). Find the strike prices K1 and K2 such that K2 ˆ’ 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 S1ˆ’ $20.50 + max(0, K1ˆ’ S1) ˆ’ max(0, S1 ˆ’ K2), where K1 and K2 are from the previous answer. What is the value of this claim? What have you constructed?

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TABLE 15.5 Table for problems. Quarter 6 Oil forward price () 210 2. 208 20.5 20. 20.0 19.9 19.8 Zero-coupon bond 0.9852 0.970 0.9546 0.9388 023 0.9075 0.8919 0.8763 price (S)