Energy Spots, Futures & Options

A futures contract is an agreement to exchange a specified quantity of a commodity at a specified date in the future. It allows the buyer and seller to lock the transaction price and avoid the uncertainty of price changes in the meantime. The modern futures market formally began in 1978. A futures option contract gives the purchaser the right to buy or sell the specified futures contract by a specified date. This mechanism allows the buyer of the options contract to limit the risk from unfavorable changes in futures prices that might occur before the option expires; the buyer essentially pays a non-refundable deposit for the option and may decline to exercise the option at the prescribed date.

Participants [top]

Two broad classifications of futures traders include (1) commercials and (2) non-commercials. Commercials are firms that actually deal in the commodity business, such as production, transportation, refining, distribution, etc. Commercials own or will own physical commodities; commercials trade in futures to hedge the costs of revenues in the course of doing business. Hedging (in this context) allows the commercial to lock the prices of inputs and outputs in order to insure a positive operating margin. For example, a refiner can lock the cost of refining operations to commence three months hence by buying crude oil (input) futures for that period. Since refining operations require about a month, the refiner can lock the revenues for those refining operations by selling refined-product futures (for outputs such as gasoline and heating oil) for four months in the futures. In this case, the difference between prices for crude futures and refined-product futures define the operating margin for refining operations that will commence three months hence. Thus, futures allow the refiner to plan with a greater level of certainty. Even if input prices were to increase (due to a crude shortage resulting from weather or OPEC restrictions) and output prices were to decrease (due to a refined-product surplus resulting from, say, a warmer than expected winter), the refiner’s profits would not fall, but remain fixed, because the profits were locked by the futures contracts (in this case, the speculators would lose).

Non-commercials are firms or individuals who do not intend to take physical possession of commodities, but rather trade futures to engage in speculation. Speculation is an attempt to predict price changes of commodities and trade futures in an effort to profit from those predictions. Speculation accounts for the majority of futures trades, as indicated by the observation that 98% of futures contracts are offset by reverse contracts prior to delivery, and only 2% of contracts result in actual delivery of commodities.

Commodity Positions [top]

Two broad classifications of commodity positions (in a market sense) include (1) futures positions and (2) spot or cash positions.

A futures position is a promise to make or take delivery of a commodity at a specified place and time in the future. A long position in futures results from purchasing contracts (committing to take delivery). A short position in futures results from selling contracts (committing to make delivery). Futures are purely financial instruments and do not imply physical possession of the commodity for any sort of industrial purpose. Futures contracts are standardized to specify the point and method of delivery upon expiration. However, failure to offset a long position in futures prior to the expiration date (i.e., having previously purchased a number of futures contracts, then failing to sell an equal number of contracts prior to the expiration date of the original contracts) will result in liquidation of the future by the broker and transfer to cash (not commodity) to the owner of the contract. Further, even if the owner chooses to take legal possession of the commodity, the commodity will be stored according to prescribed location and storage fees until the owner arranges for physical transport of the commodity from storage or sells the commodity in the cash market (at which time the cash-market buyer will transport the commodity from storage). In practice, the short futures position involves paper transaction in the form of a commitment by a commercial or non-commercial to deliver ownership of the commodity at a place and time as prescribed in a standardized contract.

A cash position implies physical possession of a commodity. A long cash position is synonymous with holding previously purchased commodity in storage. In this case, the day-to-day value of the stock changes with its price in the cash market (a.k.a. spot market). A short cash position results from an agreement or contract to deliver physical commodity. Note the distinction between a short cash position and a short futures position. In contrast to the paper transaction defined by a short futures position, the short cash position involves a physical transaction in the form of a commitment by a commercial seller to physically deliver actual commodity to a commercial buyer.

A commercial agent is net short in product if commitments to deliver commodity exceed the sum of current product inventory and futures purchased. In this case, the agent must either (1) manufacture product from input or (2) purchase products from spot markets, or (3) purchase product futures and arrange transportation upon expiration of the futures contract. Clearly, there are many scheduling variables that will constrain the agent’s choices.

A commercial agent is net short in inputs if commitments to manufacture (or transport) product require more input commodities than the agent currently holds in inventory or anticipates from input futures purchased. In this case, the agent must either (1) purchase inputs from spot markets, or (2) purchase input futures and arrange transportation upon expiration of the futures contract.

An agent is net short overall if commitments to deliver commodity exceed the sum of (1) existing product inventory, (2) product futures purchased, and (3) product anticipated from existing input inventories. For example, suppose a refiner currently holds commitments to deliver 10,000 gallons of heating oil two months hence. Further suppose the refiner holds (1) 6,000 gallons of heating oil in storage, (2) heating oil futures for 2,000 gallons to be delivered 6 weeks hence (leaving 2 weeks for transportation from the spot market), and 10,000 gallons of crude in storage (from which the refiner can manufacture at least 2,000 gallons of heating oil. In this case, the refiner is net short in product (because his long positions in both cash and futures amount to only 8,000 gallons… short of the 10,000 gallon commitment), but he is NOT net short overall because he has sufficient capacity, input (crude) inventory, and time to manufacture the missing 2,000 gallons of product (heating oil) prior to delivery deadline. If, instead, the refiner’s deadline to deliver product ware only 1 week hence (instead of 8 weeks hence), then the refiner WOULD BE net short overall, because he would not have enough time to manufacture heating oil from exist crude inventories. In this case, he would have to purchase heating oil in the spot market (or purchase heating futures expiring in a few days under agreement to actually take legal ownership of the heating oil rather than have the broker liquidate the future at expiration).

Production & Hedging [top]

Suppose the refiner above was net short in refined product (heating oil) by 2,000 gallons and had no input (crude) in inventory. The agent could rectify this discrepancy by either (1) purchasing refined product directly to reduce the commitment to manufacture, or (purchase input (crude) to enable manufacture). These choices will be driven in the short run largely by capacity utilization and production cost factors, and in the long run by capital investment decisions. However, we must understand that the commercial agent profit margin is based upon production. The shipper’s margin comes from transport crude from A to B. The refiner’s margin comes from refining crude into gasoline and heating oil. The distributor’s margin comes from contracting to deliver refine product to end-users. Thus, the commercial agent seeks to balance purchases, capacity, and production commitments across time in order to conduct smooth operation and production, and to subsequently extract a profit margin.

The commercial agent’s capital investment in fixed assets (e.g. storage tanks, pumps, refineries, etc) will define a target production capacity. If the agent, a refiner for example, over-invests in long-term assets, so that capacity always exceeds delivery agreements, then each gallon of refined product must cover an excessive fixed-cost of amortization for the excess capital equipment, which lowers average profit. Thus, in the long run, the agent must try to balance capital investment with demand expectations.

In the short run, however, the agent is constrained by existing capital assets. If the refiner gets stuck in a net short position, then he might be forced to buy crude in the spot market and operate at higher-than-normal levels of capacity utilization. Unfortunately, in general, the cost-per-gallon will increase as production levels approach and surpass target capacity. Thus, responding to a net short pinch can reduce efficiency, increase average cost, and reduce profit-per-gallon. Futures provide a mechanism for the refiner to immediately hedge each short cash position (commitment to deliver) for refined product by taking a long futures position (commitment to take possession) in crude. This is called the long hedge or buyer’s hedge. By going long in crude futures, the refiner locks the cost of crude, and can compute the profit margin on short cash positions in refined-products by subtracting the costs of transportation, storage, production, amortization of assets, and the (now known) cost of crude. At this point, the refiner is hedged against possible increases in crude prices and profit margin is locked.

In the short run, the agent is also subject to demand uncertainty. Suppose a refiner unintentionally accumulates an excess of crude so that production capacity for refined products exceeds delivery contracts (short cash positions) for refined products. The refiner can refine the crude and sell the excess product in the spot markets for gasoline and heating oil once production is complete, but this plan runs the risk of losing money on the excess product if the spot market prices for refined products fall before the refining process is complete. The refiner can hedge this risk by selling refined-product futures for the excess product, thereby locking the output price and the profit margin from existing excess crude inventories. This is called the short hedge or seller’s hedge.

Of course, the commercial agent can speculate via selectively hedging. For example, the refiner can refrain from hedging crude inputs if he anticipates that crude prices will fall before the crude must be acquired for refining operations. Similarly, the refiner can refrain from hedging refined-product outputs if he thinks the price of product in the spot markets will increase before existing crude inventories have been refined into products.

Market Structure & Activity [top]

The rules and regulations are defined in the Commodity Exchange Act (CEA) and enforced by the Commodity Futures Trading Commission (CFTC). The National Futures Associate conducts many self-regulating functions such as registration of professionals, audit, etc.

Three broad classifications of futures exchange members include: (1) commercial hedgers, (2) individual speculators, and (3) brokers. All exchange members clear their trades through a clearinghouse member. The clearinghouse tracks trade, collects & marks margins, and holds funds for collateral on deposit. Futures contracts require an initial margin of 5-10% of commodity value. If the value of commodity falls by 15-40% of original price, then the exchange makes a maintenance margin call requiring the owner to remit sufficient funds to restore the total margin deposit to the dollar value of the initial margin. The exchange assesses maintenance margins for members by marking to market; that is, by consolidating realized and unrealized gains and losses across all positions for the member. Similarly, brokers are marked to market by consolidated realized and unrealized gains and losses across all positions for all brokerage clients. Thus, unrealized gains from one position can substitute as maintenance margin for a losing position in the same portfolio. Brokers collect margin from clients and pay margin to the exchange via certified check or federal funds. Hedge accounts are granted lower margin requirements, because their futures positions are generally offset by cash positions.

If a futures position is not offset by an opposing position by the last day of trading, then the exchange either liquidates the position or transfers legal possession. Some contracts call for the close of a futures position with liquidation and cash settlement of the position based on a price determined by the exchange on the last day of trading. In other contracts, the brokerage firm facilitates a transfer of legal possession upon which the seller must deliver documentation (such as warehouse receipts and certification of quality) and the buyer is assessed with storage fees until selling the commodity in the spot market.

Brokers register with the NFA as Futures Commission Merchants (FCMs). Brokers collect market, limit, and stop orders from clients, execute those orders at the appropriate fill price, and send confirmations to the client and the clearinghouse member.

Futures & Spot Prices [top]

Futures prices tend to relate to spot prices according to the principles of parallelism & convergence. Parallelism simply means that the prices move (up & down) together… not necessarily in the same amount, but usually in the same direction. This principle is common across investment instruments usually driven by arbitrage opportunities. The relation can be seen by going to a financial website (such as yahoo or quicken) and charting almost any stock listed in the Dow-Jones Industrials (DJI) against the S&P Index (SPY) over a multi-year period. Most such charts with demonstrate parallelism because investors tend to buy a stock once they think it has become cheap relative to other stocks (hoping it will go up). Indeed, parallelism is actually a charting term; but parallelism is the result of a basic economic principle called the substitution effect. Simply put, this means that a price increase for one good will increase the demand for substitute goods. For example, if McDonald’s increase its prices, then some customers will substitute toward Burger King; which would allow Burger King to raise prices as well. With commodities, traders will tend to buy futures (rather than buy inventory and pay storage fees) when futures become cheaper relative to the current spot price, which drives up futures prices. Similarly, traders will buy commodity and hold it in inventory (rather than buy futures) when spot prices are cheap relative to futures prices, which drive up the spot prices. Thus, shocks that impact one price tend to translate to the other prices, as well, driving both prices in the same direction. Hedging also supports parallelism, since commercial hedgers usually offset their cash commodity positions with an equal and opposite futures position. For example, an unexpectedly increasing demand for gasoline will increase order to refiners and drive up gasoline spot prices. The refiners in turn go short in the cash markets for gasoline and subsequently hedge by going long in the futures market by buying gasoline futures, which increases the demand for gasoline futures and drives up gasoline futures prices. In this example, both spot & futures prices for gasoline move upward together. If demand subsides relative to supply (capacity, reserves, and available crude), then both prices will move down together.

Convergence means that spot and futures prices move closer as the futures’ expiration date arrives. This is a somewhat obvious expectation. The futures price in some fashion represents the market’s guess at what the spot price will be in the future, but the likelihood of changes in the spot prices depend on how far we look into the future. If we expect a large price swing in the future, then the futures price will rise. For example, if the market begins to anticipate that OPEC will restrict crude exports in the long run (say, after three months), then the market must subsequently anticipate a coming crude shortage and higher spot prices in the future. This will accelerate the buying of crude futures and increase futures prices. In the short-run, however, one would generally not expect spot prices tomorrow to change drastically from spot prices today… thus there is little incentive to pay much more or less for 1-day futures the today’s spot price.

Contango & Inverted Markets [top]

Generally, futures prices are higher than spot prices due to the costs of holding commodity in inventory, which is known as the carry charge and is made up of storage costs, insurance, and interest). Suppose a refiner is planning operations to commence three months hence. The refiner can either (1) purchase crude now in the cash (spot) market and pay for three months until he is ready to process the crude into refined-products, or (2) purchase 3-month crude futures. The refiner will be willing to pay more per barrel for crude futures than cash (spot) crude, because futures allow him avoid three months worth of carry charges. In this case, futures are said to sell at a premium to cash. The market is called a premium market, or carry charge market, or contango market. Generally, contango markets exhibit the following price relationships:

price^futures > price^spot

and

price^futures £ price^spot + carry charge.

The futures premium seldom equals the full carry charge, because there is often a business advantage (called convenience yield) to holding some commodity as inventory. For example, holding inventory might lower risks of unexpected performance failure on futures contracts.

An inverted market exists when the futures price is higher than the spot price. This condition occurs in the short-run due to shortages in the spot market. For example, factors such as weather might unexpectedly drive up demand for heating oil relative to refiners’ planned production. Similarly, factors related to crude imports might reduce crude supplies relative to refiner’s planned production of heating oil. Such shortages would drive up spot prices for heating oil. However, assuming that the factors causing the gap in supply and demand will be corrected in the future, causing spot prices to fall back down in the future, then futures prices will remain low… in some cases lowest than spot prices. Some markets are seasonally inverted. For example, the heating fuel market inverts in winter anticipating a decrease in demand for the spring. Similarly, the gasoline market inverts in at the end of the driving season (late summer) anticipating a decrease in demand for the fall and winter. The examples above describe inverted markets resulting from unexpected or seasonal shortages in the spot markets. However, the crude market tends to remain inverted even in equilibrium (i.e., when there is neither shortage nor surplus in the spot markets). This is accredited to a lack of storage capacity for crude. Thus, when surpluses occur, the market is penalized with excessive storage costs for crude. Refiners can avoid the risk of such penalties (in the future) by under-planning for expected demand; that is, by purchasing fewer crude futures contracts than they expect to need and waiting to satisfy the rest of their crude oil needs in the spot market of the future. This is an inter-temporal substitution in which preparations are postponed into the future to avoid the risk of unexpected surpluses and unwanted inventory. This substitution creates a sustained shortage in the spot market stemming from a lack of futures purchases in the past. The sustain shortage drives a sustained inverted market:

price^{crude futures} < price^{spot crude}.

Contango v Inverted Markets: Risk Management [top]

The argument for an inverted crude market seems contrived given that storage costs are used to explain both contango and inverted markets; storage costs result in a premium for futures in some markets but a discount for futures in other markets. To understand how this can be we consider two forms of scheduling risks: (1) surplus risk and (2) shortage risk. The commercial agent realizes surplus risk when planned production exceeds the ultimate spot demand for output commodities, resulting in storage penalties. The commercial agent realizes shortage risk when planned production falls below ultimate spot demand for output commodities, resulting in opportunity costs of lost profits for the period. The refiner plans in some fashion with respect to the likelihoods of each possible outcome. We can investigate the refiner’s risk management decision with the following over-simplistic optimization model. Let p º output price (for refined products), w º Input price (for crude), s º carry charges. For simplification, assume p, w, and s are constant across time periods. Let q_t º quantity of refined product that the refiner can sell in time period t. Let x_t-1 º be the quantity of crude oil acquired from time period [t-1].

Surplus Loss is a direct cost imposed on the commercial agent when demand for product is below planned production. In this case, the refiner might have planned to use an expected quantity of crude (x_t-1^e) for production, but only required x_t-1^low for the slumping (low-demand) market. Assume that the storage cost s is actually a function of the excess crude remaining after production.

Surplus Loss = s = s(x_t-1^e- x_t^low)

In keeping with standard observations of industrial cost functions, we assume that storage cost increases at an increasing rate with the amount of un-used crude, so that:

s’ = ¶s/¶[x_t-1^e] > 0,

and

s” = ¶²s/¶[x_t-1^e]² > 0.

Surplus Loss is an opportunity cost that occurs when demand for product is above planned production. In this case, the refiner might have planned to use an expected quantity of crude (x_t-1^e) for production, but missed the opportunity to run at full capacity and utilize x^capacity. Assume that the production of refined product q is actually a function of crude, so that the foregone revenue is a function of the refiner’s under-purchase of crude.

Shortage Loss = p×q^shortage = p×q(x^capacity- x_t-1^e) = p×q^capacity - p×q(x_t-1^e)

In keeping with standard observations of industrial production functions, we assume that production increases at a decreasing rate with the amount of crude, so that:

q’ = ¶q/¶[x_t-1^e] > 0,

and

q” = ¶²q/¶[x_t-1^e]² < 0.

The refiner seeks to minimize Risk = Shortage Risk + Surplus Risk. Let f represent the probability of Shortage Loss, so that Shortage Risk = f×Shortage Loss. Thus, (1-f) represent the probability of Surplus Loss, so that Surplus Risk = (1-f)×Surplus Loss. Optimization requires the refiner to minimize Risk = f×p×q(x^capacity- x_t-1^e) + (1-f)×s(x_t-1^e- x_t-1^low) subject to x_t-1^e £ x^capacity. For simplicity, we assume f = 50%, so that f = (1-f), but this assumption is revisited below.

We derive the following first-order condition:

¶[Risk]/¶[x_t-1^e] = -p×q’ + s’ = 0 Þ p×q’ = s’.

We verify the second-order condition for minimization:

¶²[Risk]/¶[x_t-1^e]² = -p×q” + s”, q”>0, s”>0 Þ ¶²[Risk]/¶[x_t-1^e]² >0.

In economic terms, p×q’ is known as the value of marginal product (VMP) and s’ is known as a type of marginal cost (MC). The refiner optimizes by purchasing crude futures until the expected MC of crude storage equals the expected MVP of refined products. Of course, this is only a simple model of the actual decision process, which might look very different. But this model captures some of the pressures that will continually force refiners to revise their scheduling decisions.

Inverted markets will have the following sustained risk profile, in which the total risk is minimized below the production capacity for the refinery. This occurs because the surplus risk is driving up the total risk as crude purchases approach the productive capacity of the refinery. This will cause the refiner to (1) under-schedule crude purchases in the future market in time = t-1, (2) wait to see whether there is shortage market for refined products in time = t, then (3) pay a premium for crude in the spot market at that time. Such a risk profile is depicted in the following graph.

Contango markets can be sustained in equilibrium in two cases. The first is the case when carry charges (i.e. surplus losses denoted above by s) are small relative to the value of production (i.e. shortage losses, which depend on the expected price of outputs and production efficiency). The second is the case when the likelihood of surplus is small relative to the likelihood of shortage. In our example above, we assumed equal likelihood of surplus and shortage. Both of these cases will tend to flatten the surplus risk schedule relative to the shortage risk schedule. This flattening can cause the total risk schedule to by decreasing as it approaches the production capacity for the commercial agent. Such agents minimize risk at full capacity, allowing for full substitution into futures at a premium to cash, and creating a sustained contango market. Such a risk profile is depicted in the following chart.

Options on Futures [top]

The buyer of an option pays a premium for the right to trade the underlying instrument by a certain date. The seller of an option collects a premium for becoming obligated to trade the underlying instrument if the buyer chooses to make the trade. Options take two forms in relation to the optional trade: (1) a call option gives the buyer the right to buy the underlying instrument, and (2) a put option gives the buyer the right to sell the underlying instrument. So, a call gives the buyer the right to long the future, and gives the seller the obligation to short the future. Conversely, a put gives the buyer the right to short the future, and gives the seller the obligation to long the future. For example, if one buys a call option for crude oil futures, then the buyer has the right to buy the futures at a certain price (call the strike price) by a certain date. If crude futures price rises above the strike price, then the buyer will exercise the option (buy the futures) at the strike price. At this point, the futures could be re-sold at the futures price for a gain. If the futures price exceeds the strike price by more than the premium, then the options buyer makes a profit on the transaction overall. In this example, the options buyer was bullish, expecting the futures price to go up. However, the choice of whether to buy or sell options does not depend on whether one is bullish or bearish on crude futures. A bearish trader could buy a put option… an option to sell futures if the price of crude futures falls below the strike price. In both cases, the buyer will gain if the price moves in the expected directed past the strike price. If, on the other hand, the price moves in an unexpected directed, the buyer will not exercise the option and will only be out the premium amount paid for the option. Thus, options are a means for the buyer to limit downside potential.

An option can be written at a strike price that is above, at, or below the current futures price. If the strike price is set equal to the current future price, then the option is said to be ”at-the-money” and the buyer shall remain neutral toward either exercising or abandoning the option until futures prices move up or down. An option is written ”in-the-money” if the buyer has incentive to exercise the option at the current futures price. Is this case, the buyer will not abandon the option unless futures prices move unfavorably toward and past the strike price. An option is written ”out-of-the-money” if the buyer has incentive to abandon the option at the current futures price. Is this case, the buyer will not exercise the option unless futures prices move favorably toward and past the strike price. For example, a call option is “in-the-money” when the strike price is below the current futures price, because the buyer benefits from exercising the option by buying the underlying futures contract at a discount. In contrast, a put option is “out-of-the-money” when the strike price is below the current futures price, because the buyer would lose from exercising the option by selling the underlying futures contract at a discount.

Premiums are sunk costs; that is, they do not determine whether the buyer exercises the option (once it has been purchased), but they do determine whether the exercise of an option is profitable overall. For example, suppose the current futures price for crude oil is $50 per barrel. Suppose one pays $2K in premium to buy a call option for a futures contract of 1,000 barrels of crude oil at $50K ($50 per barrel). The option is written at-the-money because the strike price ($50 per barrel) equals the current futures price. The $2K of premium is lost to the buyer as soon as the option is purchased, whether or not it is exercised. If the futures price falls below the strike price, then the buyer will abandon the option. However, suppose the futures price rises to $53 per barrel. The buyer will exercise the option to buy the futures contract for $50K, sell the contract on the futures market for $53K, and make $3K on the trade. The buyer paid $2,000 up front for the option, so the total gain is $3K - $2K = $1K. The option buyer made $1K because the futures price rose. Now, suppose the futures price rose only to $51 per barrel by the expiration date of the option. The buyer will still exercise the option to buy the futures contract for $50K, sell the contract on the futures market for $51K, and make $1K on the trade. The buyer paid $2,000 up front for the option, so the total gain is $1K - $2K = -$1K. The option buyer lost $1K because the futures price did not rise enough to cover the premium, but the buyer still exercised the option to minimize total losses. If the buyer had abandoned the option, then the total loss would have been the full $2K of up-front premium.

The worst-case for the options buyer in the previous example is a loss of the $2,000 premium (if futures prices do not rise at all). This is the purpose of buying an option… to cap your losses. NOTE: premiums do not influence the decisions of whether to exercise an option once it has been purchased, but they do influence whether or not to purchase the option in the first place. So, the buyer in the previous example will exercise the option to buy the futures if the futures prices increase above $50, but will only buy the option in the first place if he expects the price to rise higher than $52 (the minimum rise required to cover the premium).

Options Pricing & Margins [top]

The pricing of options refers to the premium rate, which is the cost of buying the option. This rates has two components. First, the intrinsic value is simply the built-in discount of those options that are written in-the-money; this is a simple calculation based on the relative strike price. Second, and more interesting, the time-value premium (TVP) is the premium the buyer pays to speculate on price changes. The TVP is the true actuarial cost of the option. I shall henceforth use the terms price and premium to refer to TVC. Option traders use pricing models (such as Black-Scholes) to determine fair-value premium based on four factors: (1) relative strike price, (2) time-to-expiration, (3) interest rates, and (4) volatility. The following discussion of these factors refers pricing of options prior to their purchase; I use the phrase “as strike prices move” to refer to a cross-sectional (point-in-time) comparison of multiple options with various strike prices. In contrast, we refer to “move in futures prices” to refer to the [inter-temporal] change in futures contract prices over the life of an options contract, from purchase to expiration.

Relative strike price refers to the relation of strike price to current futures prices. That is, the relative strike price for a call option is neutral when at-the-money, positive when in-the-money, and negative when out-of-the-money. Premiums are highest at-the-money, and decrease as strike price moves away from current futures price. Premiums decrease as strike prices move further in-the-money because the buyer must pay increasingly more to cover the intrinsic value of the option; this creates a leverage cost. The intrinsic value that is added into the cost of the option has a similar economic influence as a refundable deposit that increases with the expected discount from exercising the option. The larger the expected discount to the buyer, the more the buyer must pay up-front for the option. This counteracts one of the most attractive features of options for traders, that the can leverage a large potential gain from a relative small up-front payment. This leverage cost reduces demand and therefore premiums as strike prices move further in-the-money. Premiums decrease as strike prices move further out-of-the-money because prices are decreasingly likely to move enough to exercise the option; this creates a risk cost. This greater risk finds fewer traders willing to bear the risk, which reduces demand and therefore premiums as strike prices move further out-of-the-money.

Time-to-expiration increases the chance of favorable price changes in futures contracts; thus the buyer must pay a higher premium for a better chance of exercising a profit. Premiums increase (as a rule-of-thumb) with time-to-expiration according to the square root of duration. For example, the premium for a 6-month option will be about 40% higher than for a 3-month option (√6 / √3 = √2 ≈ 140%). Interest Rates are related to time-to-expiration, but (in principle) decrease the present value of the expected payoff from an option, and therefore impact premium rates. In practice, however, interest rates have little relative impact on options prices.

Volatility increases the chance of favorable price changes in futures contracts; thus the buyer must pay a higher premium for a better chance of exercising a profit. Volatility is generally estimated as the annual standard deviation in the log of futures-price (which approximates the percentage change). For example, let p₀ = 100 and p₁ = 115. The simple percentage change = 15%. The difference in logged prices = ( ln(p₁) - ln(p₀) ) ≈ 4.745 - 4.605 ≈ 14%, which approximates the 15% increase. Premiums are determined somewhat linearly from the annual standard deviation of such prices changes. Suppose a future whose prices have historic volatility of 20% has a premium of &1.50. If the volatility in the next year increases [by 50%] to 30%, then the premium should increase [by 50% as well] to about $2.25.

Margin requirements are deposits that must be posted to the exchange for out-of-the-money balances on outstanding options. These apply to the writer of options and are driven be volatility. Basically, if futures prices move unfavorably for the seller, the margin requirements force the seller to post additional funds as partial collateral in case the option is exercised at a loss to the seller. Margin requirements are set by the exchange, and the clearing members may set additional requirements. As a rule-of-thumb, the margin requirement for the writer equals the premium plus the underlying futures margin minus half the amount that the option is out-of-the-money, but not less than half the futures margin. The margin is reduces for out-of-money positions because the option becomes increasingly profitable for the writer as it moves further out-of-the-money.

The buyer of American options may exercise those options at any time up to expiration, whereas European options can only be exercised on the expiration date. The American practice favors the buyer, who can capitalize on any favorable price move during the contract period, even if the price move reverses prior to expiration. This advantage no doubt increases the premium for American options relative to European options.

Options Spreads & Combinations [top]

An options spread refers to trading two or more calls (or two or more puts) at different strike prices in order to benefit from a favorable move in the underlying futures price. Options spreads differ from futures spreads. Futures spreads benefit from relative price changes, such as when a trader is short crude and long gasoline and experiences a decline in the price of crude relative to the price of gasoline. Each of the following three simple options spreads whether one speculates that futures prices will rise, fall, or remain unchanged. A bull spread buys a call at-the-money and sells a call out-of-the-money. The max loss is the up-front cost of the long minus the up-front income from the short; this occurs if futures prices fail to rise and both options are abandoned. If futures prices rise then the long call starts to show a profit before the short call shows a loss; profit is capped when futures prices reach the strike price for the short call. The purpose for selling the call is to reduce the up-front premium. The cost of that reduction is a cap on the upside potential. A bull spread can be accomplished with puts as well, but put spreads are subject to margin requirements. A bear spread buys a put at-the-money and sells a put out-of-the-money. The max loss is the up-front cost of the short minus the up-front income from the long; this occurs if futures prices fail to fall and both options are abandoned. A butterfly spread buys two calls (one in-the-money and one out-of-the-money), and sells two calls at-the-money. The payoff schedule is the overlay of the previous two spreads. In this case, the trader will lose up-front premiums if futures prices either rise above the higher strike price or fall before the lower strike price. However, the trader will realize a profit if prices remain near the at-the-money strike price. Of course, the potential upside will be lower for less volatile futures.

An options combination refers to trading of both puts and calls. A long straddle buys a call and put at the same strike price. If futures prices remain at the strike price, then both options will be abandoned and the buyer will lose the up-front premium on both options. However, as futures prices move either up or down, one of the options will be exercised with unlimited upside potential while the other is abandoned. If prices move enough to cover the premium on both options, then the buyer realizes a profit. Long straddles are not subject to margin requirements, because the max loss is limited and equal to the up-front premium on both options. A short straddle writes a call and put at the same strike price. If futures prices remain at the strike price, then both options will be abandoned and the seller will keep the up-front premium on both options; this is the best-case scenario for the short straddle. If prices move, however, then one of the options will be exercised against the seller. If prices move enough to cover the up-front premium, then the seller begins to realize a net loss. If prices keep moving, then the loss increases without limit. Since losses are not capped, short straddles are subject to margin requirements. A long strangle is similar to a long straddle, except the options are purchased at different strike prices. This approach lowers the buyer’s up-front premium (max loss) by not trading at-the-money (see previous discussion of leverage cost and risk cost), but it also requires greater price moves for the buyer to realize a profit. A short strangle lowers the up up-front premium (max gain) to the seller by not trading at-the-money, but it also lowers the risk to the seller by requiring greater price moves before the seller realizes a loss.