A bond issued by Standard Oil some time ago worked as...

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 $$\$ 2,550$$ (which corresponds to a price of $$\$ 40$$ per barrel). Show that the bond is a combination of a regular bond, a long position in call options on oil with a strike price of $$\$ 25$$, and a short position in call options on oil with a strike price of $$\$ 40$$.

Key Concepts

Long and Short Positions in Options

A long position in an option implies holding the right to benefit from favorable movements in the underlying asset's price, whereas a short position implies an obligation to deliver if the option is exercised. This combination allows the bond issuer to structure the payout so that the investor gains if oil prices exceed $25, but the gains are limited when prices exceed $40.

Bond

A bond is a fixed income financial instrument that represents a loan made by an investor to a borrower. In this context, the bond promises to repay a predetermined amount of money at maturity, independently of any additional variable payments. It serves as the core, risk-free component of the investment.

Call Option

A call option is a derivative that gives its holder the right, but not the obligation, to buy an asset at a specified price within a certain period. Here, the option is used to model the additional payment based on the oil price, capturing the upside potential if oil prices rise above a certain level.

Strike Price

The strike price is the predetermined price at which the holder of a call option can purchase the underlying asset. In the bond's structure, the call options have strike prices that determine when and how the additional payments kick in, specifically at $25 and $40 per barrel.

Call Spread

A call spread involves taking a long position in a call option at a lower strike price and a short position in another call option with a higher strike price. In this problem, the bond's payoff is engineered as a spread: the investor benefits from oil prices over $25 (long call) but is offset when oil prices exceed $40 (short call), thus capping the maximum additional payment.

Payoff Decomposition

Payoff decomposition refers to breaking down a complex financial instrument's payoff into simpler components. In this question, the bond's overall payoff is decomposed into a standard bond component and a derivative component consisting of a call spread. This decomposition aids in understanding and replicating the bond's payoff using basic financial instruments.

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