Question

A bond issued by Standard Oil some time ago worked as follows. The holder received no interest. 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) of the price of a barrel of oil at maturity over $25. The maximum additional amount paid was $2,550. Show that the bond is a combination of a regular bond, a long position in call option on oil with a strike price of $25, and a short position in call on oil with a strike price of $40.

Answer 1

The bond is a mix of a zero-coupon bond, a call option on oil with a strike price of $25 (long), and a call option on oil with a strike price of $40 (short). This structure guarantees a base payout at maturity, with additional profits if the oil price is above $25, but caps the maximum payout if oil exceeds $40.

Step-by-step explanation:

The bond in question is a combination of a zero-coupon bond, a long position in a call option on oil with a $25 strike price, and a short position in a call option with a $40 strike price. The concept is best understood through financial derivatives. A zero-coupon bond will pay out the face value of $1,000 at maturity.

A long call option gives the buyer the right, but not the obligation, to purchase oil at $25 per barrel; if the oil price is above this at maturity, the payout is the difference, multiplied by 170 barrels. The bond caps the additional amount at $2,550, which corresponds to an oil price of $40 per barrel ($40 - $25 = $15, $15 x 170 = $2,550), hence the short call option position. This short option means if the oil price exceeds $40, the bond issuer will not have to pay more despite further increases in oil prices.