Standard Oil issued a non-standard bond to raise capital in the following way. A

Question

Standard Oil issued a non-standard bond to raise capital in the following way. At the bond’s maturity the company promised to pay $1,000 plus an additional amount based on the price of oil at that time. The additional amount was equal to the product of 170 and the excess (if any) price of a barrel of oil at maturity over $25. The maximal additional amount paid was $2,550 (which corresponds to a price of $40 per barrel). Show graphically that this nonstandard bond can be replicated (or is equivalent to) a combination of a standard zero coupon bond with face value of $1,000 plus two positions in options. What are the two option positions required to replicate this bond?

Explanation / Answer

Let ST be the price of oil at the bonds maturity. The addition to $1000 the standard oil pays

0 ST < $25

170(ST -25) 25 < ST < 40

2, 550 40 < ST

This is a payoff from 170 call options on oil with a strike price of 25 less the payoff from 170 call options on oil with a strike price of 40. Thus the the bond is equivalent to a regular bond plus a long position in 170 call options on oil with a strike price of $25 plus a short position in 170 call options on oil with a strike price of $40.

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