Derivatives of derivatives

In the second article in a series on basic risk management products we continue the derivatives theme with a look at energy options.

Last month we looked at derivatives – specifically, the simplest of derivatives, futures contracts (see EPRM November 2001, pages 25–27 - click here). Here we expand on the subject of derivatives, this time discussing a subset of futures contracts – options.

We will focus on instruments that exist as a result of an underlying futures contract – that is, based on an exchange-traded instrument. In practice, however, an option is a generic term used to describe the right but not the obligation to receive or deliver some other product, whether a physical commodity or a financial instrument. The key here is ‘right but not obligation’.

CALLS AND PUTS

Insofar as a definition is concerned, options may then seem fairly straight-forward. But if we consider that for every buyer there must be a seller, things get a little more complex.

In buying a call option, the buyer purchases the right to receive a futures contract. The seller then has a relationship opposite to that of the buyer. That is, the seller must have the obligation to deliver a futures contract to the buyer.

But why sell these rights? The answer is simple: money. The buyer pays a premium to the seller for the latter’s rights. Calls are usually bought as a hedge against rising commodity prices. Calls are then sold when the seller thinks prices might drop slightly and wishes to collect money from this movement.

However, selling a call only provides limited protection. This protection is limited to the premium collected from the sale of the option. The seller has exchanged the collection of the premium for upside participation.

Figure 1 more clearly shows the relationship between buyer and seller. Note the opposing profit/loss profiles of the buyer (who is taking a long position) and the seller (who is taking a short position). A dollar profit for the buyer is a dollar loss for the seller. Granted this profit/loss is partially offset by the premium, but we will always have a cancelling effect between the buyer and seller.

Buyer and seller also have opposing views and relationships with regard to puts. The buyer of a put has the right to deliver a futures contract to the seller. If the buyer has the right to deliver, the seller must have the obligation to receive. Once again, the buyer is buying the right from the seller. The buyer has paid a premium to the seller for this right.

Puts are usually bought as a hedge against falling commodity prices. Puts are generally sold when the buyer thinks prices might rise slightly and wants to collect money to help offset that rise (see figure 2). Once again, the protection is limited to the premium collected.

LONG OR SHORT?

Our discussion in the November issue about long and short positions is relevant to a discussion of the buying and selling of of puts and calls. The buyer is said to be long tht option, while the seller is said to be short. Ther eis also a potential long or short underlying future position.

Table 1 helps to better describe this potential underlying position. The buyer of puts and calls will always have the right to accept the underlying, as opposed to the seller, who has the obligation to provide the underlying.

We have seen that an option has a premium that is paid to the seller in order for the buyer to obtain the right to the option. The potential loss to the buyer – or holder – of the option is limited to the premium paid. The seller – or writer – has the opposite relationship. They have unlimited loss potential on the option. This unlimited financial loss can be at least partially offset by collection of the premium. Moreover, when used as a hedge, the sale of an option has a somewhat limited loss potential when netted against the physical commodity.

STRIKE PRICE

There is more to an option than just an exchange of premium. Options also have a price at which they start to serve their purpose – known as the strike price. The strike price is a value agreed upon when the option is purchased and is fixed for the length of the option. This is compared against the underlying commodity price to determine if the option has any value.

As an example, let us assume we have bought a natural gas call option for the month of December. The October 15, 2001 New York Mercantile Exchange (Nymex) futures price for December natural gas is trading at $2.83 per million British thermal units (mmBtu). We could purchase a call option with a $3.00/mmBtu strike price, paying a premium of $.212/mmBtu, thereby guaranteeing we will not pay more than $3 for December gas. Figure 3 shows the profit/loss profile of such a call.

The benefit to us is that if the Nymex price moves higher than $3, we will not pay more than the strike price plus the premium for our natural gas. Conversely, should the Nymex price finish lower than $3, we lose the premium paid for the option but retain the right to purchase at the lower market price.

Effectively, this call option has set a cap on the price we will pay for our gas. Figure 4 shows the effective purchase price of the physical commodity with the $3 call option.

As we delve deeper into options, we should be aware of the terms in-the-money, at-the-money and out-of-the-money, which describe the relationship of the underlying futures price with the strike price of the option.

For call options, the option is in-the-money when the futures price is higher than the strike price of the option. Consider a natural gas call at $3 with the underlying futures trading at $4. You have the right to buy at $3 natural gas that is now worth $4. This is clearly a favourable position. This option is in-the-money by $1. An out-of-the-money call is just the opposite – the strike price is greater than the futures price. An at-the-money option is the option that is closest to being in-the-money, while still being considered out-of-the-money.

Put options are considered in-the-money when the futures price is lower than the strike price. Puts are out-of-the-money when the strike price is lower than the futures price. Finally, a put is the option that is closest to being in-the-money, while still being considered out-of-the-money.

In our above example (the in-the-money call), the option had $1 worth of value. This $1 is called the option’s 'intrinsic value'. Literally, what is the face value of the option? In this case the option is worth $1 – that is, the difference between the futures price and the option strike price.

So while an in-the-money put or call will have some intrinsic value, at-the-money and out-of-the-money options will not have any intrinsic value. We should note, however, an option having no intrinsic value does not imply it will be given away for nothing. There is a secondary component to an option’s premium: time.

Time or 'extrinsic value' affects the value of the option. It is this time component that gives sellers the chance to recoup some of the exposure to selling an option today and having to incur x number of days’ price fluctuation (x being the number of days until expiration).

The big issue with regard to pricing options is how much to charge for time? What is time worth when we write an option? To answer this we have to turn to option pricing theory.

Option prices – or premiums – are not just randomly chosen numbers, but mathematically derived values. Mathematical models have been developed to assist in deriving option premiums. The most famous of these models is the Black-Scholes (equities) model, or simply the Black (commodities) model. This model, like so many others, attempts to derive a fair value for the time component of an option’s premium. The problem is that no single element affects an options value.

Five common factors have been identified that will cause an option’s premium to change and therefore allow for a value to be derived. These factors are: strike price, time until expiration, underlying price, volatility, and risk-free rate of return.

The strike price and its relationship to the underlying price will determine whether the option has any intrinsic value. We can determine extrinsic value depending on how much time is left in the option before expiration and on the perceived volatility in the market-place.

This is precisely the aim of mathematical models – to derive a probability distribution around the underlying instrument’s prices, given time and volatility, so that we can better value the amount of risk between today and the expiration date. This risk will directly translate into a 'time premium' or extrinsic value for our option.

The problem is that everyone has a different assumption of what volatility is or should be. Volatility is simply a measure of the speed and range of price movement in the underlying instrument. Unfortunately, simple as this definition sounds, volatility is the most subjective element of option pricing. For this reason, options are still subject to supply-and-demand forces regardless of any calculations we make.

FLEXIBILITY

Remember that an option allows us flexibility not afforded by a futures contract. This flexibility allows us the right to the underlying, but not the obligation to accept it. When a buyer chooses to convert their option into the futures contract, it is understood that they have exercised their right to the underlying futures contract. The option they once had disappears and is replaced by the corresponding futures contract.

Buyers of options are the only ones with rights and as a result are the only party to exercise the option. Sellers have the obligation to perform and therefore cannot exercise. Sellers are assigned the futures position that corresponds to the option sold.

There are also rules governing when exercise of the option may take place. These rules are dictated by the exchange the option is traded on and fall into one of two categories:

• the American-style option, for which exercise may occur at any time during the life of the option, right up to expiration; or
• the European-style option, which allows the option to be exercised only on the day of expiration.

In short, options offer us another risk management tool – one that offers flexibility that futures contracts do not: the right to a level of price protection but not the obligation to accept/receive it. Options present almost endless possibilities with which to hedge away price exposure.

Dan Rowe is senior energy consultant at The Oxford Princeton Programme, headquartered in Princeton, New Jersey. He is based in Plainfield, Illinois.
email: drowe@oxfordprinceton.com

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