Commodity Hedging for Producers and Consumers

Commodity Futures Properties

General Features

The commodity futures against maturity date has many complex features. The simpler financial assets that we considered earlier has quite simple forward curveswhen they were simple assets, even with dividends or continuous yields. $\\[10pt]$

Commodity futures have many differences to these simple financial assets. Futures markets are forward looking and the futures price will embed expectations about the future spot price. If spot prices are expected to be much higher at the maturity of the futures contract than they are today, the current futures price will be set at a high level relative to the current spot price. An upward sloping futures curve. A lower expected spot prices in the future will be reflected in a low current futures price. A downward sloping futures curve.$\\$

What return can an investor in futures expect to earn if he does not benefit from expected spot price movements, set by the market and thus that is hard or impossble to outperform on average? The answer is the risk premium: the difference between the current futures price and the expected future spot price. If today’s futures price is set below the expected future spot price, a purchaser of futures will on average earn money. If the futures price is set above the expected future spot price, a seller of futures will earn a risk premium. The question is does the risk premium exist?$\\$

Are there any theoretical reasons for the risk premium to accrue to either buyers or sellers of futures contracts? Keynes’ (1930) and Hicks’ (1939) theory of normal backwardation postulated that the risk premium would on average accrue to the buyers of futures. $\\$

"Backwardation" and "contango" are two terms used to describe the relationship between expected future spot prices and actual futures prices. When a market is in contango, the futures price is above the expected spot price. When a market is in normal backwardation, the futures price is below the expected future spot price. $\\$

Backwardation

The existence of backwardation has several explanations. An extensive literature exists concerning the drivers of commodity returns and backwardation in particular. Keynes [1930] developed the classical theory of backwardation-driven commodities futures prices, wherein backwardation arises because of the risk aversion of commodity inventory holders. Hicks [1946] agreed with Keynes that hedgers were more likely to be short because commodity inventory holders would be in a more vulnerable position than consumers and so will be under more pressure to hedge than consumers.$\\$

Producers of commodities would seek to hedge the price risk of their output. For example, a producer of grain would sell grain futures to lock in the future price of his crops and obtain insurance against the price risk of grain at harvest time. Speculators would provide this insurance and buy futures, but demand a futures price which is below the spot price that could be expected to prevail at the maturity of the futures contract. By “backwardating” the futures price relative to the expected future spot price, speculators would receive a risk premium from producers for assuming the risk of future price fluctuations. $\\$

A risk premium is the investment return an asset is expected to yield in excess of the risk-free rate of return. An asset's risk premium is a form of compensation for investors. It represents payment to investors for tolerating the extra risk in a given investment over that of a risk-free asset. $\\$

In the classical model of commodity futures pricing, which was successively developed by Kaldor [1939], Working [1948], Brennan [1958]the return from purchasing a commodity and selling it for future delivery, should, in the absence of arbitrage, equal the interest forgone plus the marginal storage cost less the marginal convenience yield for holding an inventory. This pricing model is also known as the theory of storage. For commodity markets to become backwardated, the convenience yield from holding the physical commodity must exceed the cost of physical storage plus the interest forgone. $\\$

The modern theory of commodity pricing could be considered to start with Kaldor [1939] and Working [1948]. Kaldor reasoned that there are actually two types of yields for a commodity inventory holder. One is the cost of financing and storing inventories (or stocks); and the other is the benefit of being able to use the inventories the moment that they are commercially needed. The latter benefit became known as the “convenience yield”.$\\$

Working considered risk aversion to be only one source of hedging demand. Working explained the difference between spot and futures prices by the cost of storage. Working believed that the risk-premia explanation for commodity-futures-price relationships had been over emphasised. Instead, he considered backwardation to be the result of a convenience yield that accrues to the holder of a commodity during periods of low inventory $\\$

Kaldor noted that during backwardation, holding a physical position seems, at first glance, to be illogical, since it is clear from the futures market that prices are expected to fall. Why not simply buy later at a lower price, or buy a long-dated future rather than buy in the spot market? He introduced the term “convenience yield”, i.e., the convenience or benefit derived from holding the physical commodity rather than a paper futures contract. This was measured as a percentage yield (as proposed by Working) which the holder of the physical asset implicitly receives to offset the decline in price.

Backwardation can occur as a result of a higher demand for an asset currently than the contracts maturing in the coming months through the futures market. Traders use backwardation to makea profit by selling short at the current price and buying atthe lower futures price

Inventories

One of the fundamental drivers of the price of crude oil is inventories. Since crude oil is a storable commodity, stocks play a central role in the intertemporal relationship linking current demand and supply to expectations of future demand and supply. Storing oil is intrinsically valuable because of the operational flexibility that stocks provide to refiners by reducing the costs of changing production and helping them to avoid stockouts. Consequently, the optimal levels of production and inventories are jointly determined given the spot price of oil and the price of storage (Pindyck 2001). $\\$

While the price of storage is not directly observable, it is closely related to the oil convenience yield. The convenience yield can be thought of as the interest rate paid in barrels of oil for borrowing one barrel of oil, and it can be constructed from the prices of crude oil futures contracts. The borrower of a barrel of oil is, in essence, supplying storage in the form of crude oil inventories to the lender. As a result, the lender must be compensated for forgoing the benefits associated with holding the barrel of oil. In equilibrium, this condition links the convenience yield to the price of storage, and periods of relative scarcity of the commodity are related to high convenience yields. The relationship between the short-term convenience yield and the current level of inventories, or the so-called Working curve$\\$

Consistent with the theory of storage, longer-maturity convenience yields are forward-looking variables related to the scarcity of the commodity. The term structure of convenience yields (futures contracts increasing in expiry date) contains information about future crude oil production, global real economic activity and the real price of crude oil.(Gorton, Hayashi and Rouwenhurst 2012).

Example: Wheat Producer

When you hedge your wheat production by selling a futures contract at what appears to be “zero cost,” you are essentially exchanging one type of risk for another. Although the futures contract is structured to have zero net value at inception (meaning that, on average, neither party expects to make a profit from the contract alone), the act of hedging changes the risk profile of your overall position. Here’s how to interpret it as a zero-sum game:

The Nature of Futures Contracts:
- A futures contract is a zero-sum instrument. Whatever one party gains from price movements in the contract, the counterparty loses by the same amount.
- At the start, the contract is entered at a price that makes its initial value zero. Neither side pays an upfront premium (unlike an option, where you might pay a premium for downside protection).
What you are giving up:
- As a wheat producer, without a hedge, your revenue in a year is uncertain—you face the possibility of both high and low wheat prices.
- By selling a futures contract, you lock in a selling price (the forward price) for a portion or all of your production. This reduces the variance (risk) in your revenue.
- However, this hedge also means you give up the opportunity to benefit from any price increases above the forward price. In other words, you exchange the upside potential (as well as the downside risk) for certainty.
The Zero-Sum Transfer of Risk:
- The party on the other side of your futures contract (the counterparty) is taking on the price risk that you have given up.
- If prices rise, you lose on the futures contract (offsetting your higher revenues from selling wheat), while the counterparty gains. Conversely, if prices fall, you gain on the futures contract (offsetting your lower wheat revenues), while the counterparty loses.
- In aggregate, any gains or losses on the futures contract cancel out between the two parties—this is the essence of a zero-sum game.
The “Cost” of Hedging:
- Although there is no explicit cost (like a premium) for entering the futures contract, you are still “paying” by sacrificing the optionality of benefiting from favorable price movements.
- The risk premium or the “option value” embedded in holding an unhedged position is what you give up. That value is effectively transferred to the counterparty, who is willing to accept the risk in hopes of a favorable outcome.
Risk Preferences and Utility:
- It’s important to note that while the futures contract itself is zero-sum, hedging can be very valuable for risk-averse producers. Even though you might forgo some potential upside, the reduction in uncertainty can be worth more in utility (or peace of mind) than the potential gains from price volatility.
- In other words, the “cost” is not an explicit dollar cost, but rather the loss of the chance to benefit from favorable market moves. For someone who values stability, this is a beneficial trade.

When you hedge with a sold futures contract:

You trade uncertainty for certainty: You give up the possibility of extra gains from rising prices in exchange for protection against falling prices.
The futures contract itself is zero-sum: Every gain you lose (or vice versa) is exactly balanced by a gain (or loss) to the counterparty.
The “cost” of hedging is the loss of optionality: While the contract costs nothing upfront, it alters your revenue distribution by removing the upside potential, which is the “price” you pay for reducing risk.

Thus, even though the hedge is entered at zero cost in terms of the contract’s value, you are still transferring risk (and potential reward) from yourself to another party. This transfer is perfectly zero-sum, as the gains and losses on the futures contract offset one another, even as they change the risk profile of your overall position.

When you hedge your wheat production by selling a futures contract, you're not eliminating risk from the market—you're shifting it. Here’s a breakdown of the risk transfer and how that risk manifests:

Price Risk Reduction for the Producer:
- Before Hedging:
  Without a hedge, your revenue is fully exposed to fluctuations in wheat prices. If the market price falls, your revenue declines; if it rises, you benefit from the higher prices.
- After Hedging:
  By selling a futures contract, you lock in a price for your wheat. This means that any adverse movement (i.e., a drop in the wheat price) will be offset by a gain on your futures position, thus stabilizing your revenue. Conversely, if prices rise, the gain in your cash market is offset by a loss on your futures contract.
Risk Transferred to the Counterparty:
- The other side of your futures contract (often a speculator or someone with an opposing risk exposure) takes on the risk of the wheat price moving away from the locked-in forward price.
- If Prices Fall:
  You gain on the futures contract (offsetting the loss in the cash market), while the counterparty loses.
- If Prices Rise:
  You lose on the futures contract (offsetting the gain in the cash market), while the counterparty gains.
- In either case, the risk—the uncertainty of wheat price movements—is not eliminated but shifted from you to your counterparty. This is the essence of a zero-sum transaction: one party's gain is exactly the other's loss.

The Nature of the Transferred Risk:

Market (Price) Volatility Risk:
The key risk you're transferring is the volatility or uncertainty in the wheat market. Without the hedge, you’re exposed to both the downside (if prices fall) and the upside (if prices rise). With the hedge, you forgo the upside potential to avoid the downside risk.
Implicit Optionality:
In an unhedged position, you essentially have an "option" to benefit from favorable price movements. When you hedge, you give up this optionality. That lost potential gain is, in effect, the risk (or opportunity) that is transferred to the counterparty.
Basis Risk (if applicable):
In practice, if the price of the futures contract does not perfectly track the spot price of wheat, there is an additional risk called basis risk. Even though this risk is typically small when the futures closely track the underlying asset, it is another form of price risk that can manifest if the correlation isn’t perfect.

How the Risk Manifests in Outcomes:

Locked-in Price:
Your revenue becomes centered around the forward price set by the futures contract. Any movement in the market away from this forward price is neutralized by the futures settlement, so you see far less volatility in your final revenue.
Counterparty’s Exposure:
The counterparty’s profits and losses on the futures contract mirror the changes in wheat prices. If the market moves sharply, they experience corresponding gains or losses. Their exposure is exactly the risk you’ve chosen to avoid.
Zero-Sum Game:
For every dollar you “lose” on the futures contract in a rising market, the counterparty “gains” that dollar, and vice versa. The overall picture is one where the risk (and the potential rewards) is merely reallocated between market participants.

By hedging with a short futures contract, you are transferring the uncertainty of future wheat prices—that is, the risk of price volatility—from your own revenue to another market participant. This risk manifests as gains or losses on the futures contract that exactly offset changes in the spot price of wheat, leading to a more predictable (but potentially lower on the upside) revenue stream for you. Meanwhile, the counterparty takes on the full brunt of that market volatility, standing to profit if the market moves in their favor or to incur losses if it moves against them.

Risk Premia in Futures Contracts

In theory a counterparty—especially if they're a speculator who doesn’t have the same detailed knowledge of the production risks—might require compensation for taking on that risk. However, in a well-functioning futures market, this “compensation” is built into the contract pricing rather than being an explicit upfront fee. Here’s how that works:

Embedded Risk Premium in Futures Pricing:
- Zero-Cost at Inception:
  Futures contracts are typically entered at zero net cost, meaning neither side pays an upfront premium.
- Expectations and the Risk Premium:
  The futures price isn’t set arbitrarily; it reflects the market’s consensus on the future spot price adjusted for factors like the cost of carry (storage, financing costs, etc.) and any risk premium. If speculators feel they are taking on additional risk—whether due to market volatility or a perceived informational disadvantage—their required compensation shows up in the futures price relative to what the “unbiased” future spot price might be.
- Risk Premium Interpretation:
  This risk premium can be seen as the extra expected return that speculators demand for bearing the uncertainty of price movements. It’s the market’s way of compensating them for potential adverse outcomes and any adverse selection (if they believe hedgers have superior information).
How Extra Compensation Manifests:
- Adjustment of Futures Prices:
  If speculators are wary that hedgers (like wheat producers) might have better insight into future supply or cost conditions, they might require a higher expected return. This extra required return influences the equilibrium futures price. In other words, the futures price might be set such that it “penalizes” the hedger slightly—reflecting the risk premium that speculators demand.
- Market Equilibrium:
  In an efficient market, many participants (both hedgers and speculators) interact. If speculators consistently demanded a higher premium due to perceived informational disadvantages, the futures price would adjust. This adjustment ensures that, on average, speculators receive compensation that offsets the risk they assume. Essentially, the premium is not an extra fee but a built-in feature of how the futures price converges to the market’s collective expectations.
No Direct Premium Payment:
- Sacrifice of Optionality:
  For the hedger, the “cost” of hedging isn’t an upfront premium but rather the loss of the upside potential if the market moves favorably. The hedger is effectively trading the possibility of higher gains for more predictable revenue.
- Counterparty’s Expected Return:
  Speculators, on the other hand, accept that the risk they’re taking might lead to losses in some scenarios. To be enticed to take on this risk, they expect—over time—a net positive return that compensates for periods when the market moves against them. This expected return is what you could call the risk premium and it’s implicitly baked into the futures prices.
Adverse Selection and Information Asymmetry:
- Perception of Superior Knowledge:
  If speculators believe that hedgers possess superior information about future market conditions (for example, inside knowledge of crop yields or costs), they might be cautious. In such a scenario, speculators would demand a higher expected return as compensation for the risk of trading with someone who may have an informational edge.
- Market Response:
  In liquid, transparent futures markets, however, it’s difficult for one side to consistently exploit informational advantages because many market participants are well-informed and trade frequently. Competition among speculators tends to erode persistent advantages, and any required premium gets reflected in the equilibrium pricing.

While a counterparty (speculator) might theoretically require extra compensation for taking on the risk transferred by a hedger—especially if they suspect the hedger has superior information—this compensation doesn’t come as an explicit fee. Instead, it is embedded in the pricing dynamics of the futures market through the risk premium. In equilibrium, the futures price adjusts so that speculators receive an expected return that compensates them for the risk of price volatility and any perceived informational disadvantage, maintaining the zero-sum nature of the contract overall.

Commodity Futures Contracts

Basics

Futures contracts are standardizedagreements for 2 counterparties to exchange for a price an asset forspecific amounts, a future delivery dates,with quality specifictions and at a location(s). Unlike OTC forward contracts mitigatecredit riskby transacting within a regulated clearing house which has a system of marking to market and margin payments, and a system of price limits. A futures marginis the amount of money that you must deposit and keep on hand with your broker when you open afuturescontract.Like forward contracts, the futures price is established so that the initial value of a futures contract is zero.

An exchange-traded futures contract specifies the quality, quantity, physical delivery time and location for the given product. This product can be an agricultural commodity, such as 5,000 bushels of corn to be delivered in the month of March,or delivery in Cushing, Oklahoma for crude oil specified inthe NYMEX benchmark Light Sweet Crude Oil futures contract.Not all futures contracts require physical delivery of a commodity, and many are instead settled in cash. The delivery month of a derivative may also be called the contract month.The number of contracts outstanding at any time is known as the open interest at that time.

The clearing house guarantees the settlement of the contracts and any other transactions and is theformal counterparty to every transaction. The only credit risk is therefore with the clearing house.The clearing house withstands all the credit risk involved in being the counterparty to every transaction, by using the system of daily marking to market.

The credit risk is mitigated this way. At the end of every day's trading, the profits or losses accruing to the counterparties as a result of that day is change in the futures price have to be received or paid. The credit risk to the clearing house has now disappeared because accumulated losses are not allowed to build up.Failure to pay the daily loss results in default and the closure of the contract against the defaulting party.

A standardized contract is very beneficial as that it can be traded in lot sizes and can support quite large volumes and thus supply liquidity to the market.It is also possible to unwind (or offset) a futures contract at any time by performing a reversing trade, so futures contracts are extremely liquid (at least for the near maturing contracts).The exchanges allow efficient interaction between the anonomous buyers and sellers.

Unlike forward contracts, futures contracts are marked to market daily which means a price for the contract is published intra day and after trading has close. This price can be compared to the initial price entered in to. As futures prices change daily cash flows are made, and the contract rewritten in such a way that the value of that future contracts at the end of each day still remains zero.

Selling a futures contract is equivalent to taking a short position whilstbuying a futures contract means taking a long position.

The long position profits when the futures price rises
The short position profits when the futures price falls$\\$

These have the same payoff's as the long andshort forward positions.

The initial deposit that each counterparty must make when the contract is first taken out is known as the initial margin and is set equal to the maximum daily loss that is likely to arise on the contract. It varies from asset by asset and so the historical higher volatility asset classes attract ahigher initial margin e.g.commodities. $\\$

Futures contracts also have daily settlements through the daily mark-to-market process. Each day, the parties to the transaction must maintain their margin accounts. As the price of the contract goes against one of the counterparties, the loss is taken from the initial margin account and is paid over to the other counterparties marginas profit. As the margin account falls below a particular threshold (called the maintenance margin level), the exchange requires that the counterparty needs to make additional payments known as variation margin that match the initial margin account.

This daily margin cash flowmechanism thus produces the payoff an equivalent equivalent forward contract. That is daily value of the 'forward' contract is in the margin account. The exchange clears this amount to the appropriate counterparty depending on who is to receive it if the counterparty defaults or more typically at the futures expiry date.

There is a strong relationship beween spot prices and futures prices. At the expiration date, a futures contract that calls for immediate settlement, should have a futures price equal to the spot price. Arbitrage can occur otherwise. However before settlement, futures and spot prices need not be the same due to many factors. The difference between the spot and the futures price is called the basis of the futures contract. It converges to zero as the contract approaches maturity. To understand how futures prices are established requires understanding the behavior of the basis.

Basis is very important with regard to usingfutures contracts for hedging. Typically one cannot create a perfect hedge that is when the loss on your spot/cash position is not exactly offset by the gain in the futures position. The main reasons for this are

One may hedgea cash position with the 'best'futures contract available. This is because a futures contract for your riskposition may not be available so a highly correlated alternative may be used due liquidity reasons for example.
Aquality option riskexists. For wheat futures for example, you may use a futures contract that may call for delivery of a number of different types of wheat and it is uncertain what theactual quality will be delivered. Somefutures contracts contain quality options whereby the short position has the choice of delivering one of an acceptable set of assets In interest rate futures sich as bonds and T-Billsthere a are a whole range of instruments that are available for delivery
Thereexists also atiming option that is related to the quality option.Most futures call for delivery within the contract month. It is unclear if a short position will deliver the underlying asset.
Another risk risk is locational basis risk. This is mainly applicable to agricultural commodities and physical settled contracts which require specific delivery locations. There could be a difference the cash price of the good that you are sellingand the futures price at a different location. These differential basis amounts are usually providing by regulatory bodies.

A common way of closing a futures position and avoiding physical delivery is to execute a roll forward to extend the contract's maturity. This is subject to basis risk becasue we are closing then reopening the futures contract.Conventional wisdom says that best practices for all traders is to be out two trading days before the First Notice Day defined below. Traders who still want to be long can always roll forward into the next month.

If a futures trader wants to offset or liquidate a position, the delivery months must match. Most futures positions are excited prior to the delivery month, so the contracts that are close to delivery often see the most volume and set the current price of the underlying commodity. If they don't match, the trader ends up long one month and short a different month instead of canceling out the position.

In summary the main features of commodity futures are (source: Commodity Futures trading Commission - CFTC) $\\$

A commodity futures contract is an agreement to buy or sell a particular commodity at a future date
The price and the amount of the commodity are fixed at the time of the agreement
Most contracts contemplate that the agreement will be fulfilled by actual delivery of the commodity
Some contracts allow cash settlement in lieu of delivery
Most contracts are liquidated before the delivery date
A commodity futures option gives the purchaser the right to buy or sell a particular futures contract at a future date for a particular price
With limited exceptions, commodity futures and options must be traded through an exchange by persons and firms who are registered with the CFTC $\\$

Most participants in the futures markets are

commercial or institutional (providing OTC hedging or investor products).This is important as the OTC contracts are linked back to the prices ofexchange contracts. OTC's are not the same contract so the forward rate will differ from the futures price.
producers or consumers wishing to hedge their natural risk position with futures rather with OTC's. This would be problematic for counterparties outside the country where the exchange resides due to FX risk.
Speculatorswho typically arethe buyers of a hedgers sold position (for example), and attempt to profit from price changes in futures contracts. They may expect a risk premium for taking onthis risk.Though whether this risk premium exists is controversial even in the FX futures market. $\\[3pt]$

Delivery Month

The term delivery month is key characteristic of a futures contract that designates when the contract expires, and when the underlying asset must be delivered or settled. The exchange on which the futures contract is traded also establishes a delivery location and the date within the delivery month when the delivery can take place.
Not all futures contracts require physical delivery of a commodity, and many are instead settled in cash. The delivery month of a derivative may also be called the contract month.$\\$

The delivery month denotes when a derivatives contract expires, and when the underlying asset must be delivered or settled.
Delivery months are represented by a single, specific letter in the contract symbol, and delivery dates are displayed by exchanges.
Traders must exit their position as close to the delivery month as possible; otherwise, they must take or make delivery of the underlying asset.
Understanding Delivery Months

For instance, cocoa will only have delivery months occurring in March, May, July, September, or December.1This means if you do not exit your position by the end of the month before the contract's expiration, you must take physical delivery of the cocoa—or the commodity in question. Certain commodities, as noted above, can be delivered year-round.

Traders must exit their position by the end of the month before the expiration or take a physical delivery of the commodity.

Indicating the Delivery Month
Delivery months are represented by a single, specific letter in the contract, and are depicted alphabetically starting with January ("F") and ending with December ("Z").

Since futures contracts are traded on exchanges, the exchange will display the delivery date. This is the final date by which the futures contract for a commodity must be delivered. The delivery date is indicated by a letter on the ticker. Although letters are omitted, the coding system runs in alphabetical order with "Z," for example, corresponding with December:

The main delivery months for some commodities, like corn futures, are March, May, July, September, and December. They do not occur every month. These contracts are coded by the exchange such that the last two symbols denote the month and year of the delivery date. For example, a contract with a delivery date of March 2019, and the commodity has a code CL thenwould have the code CLH9. Other monthly delivery symbols are June (M), September (U), and December (Z) etc, followed by a number that represents the delivery year.

Month Codes

Month	Ticker
JAN	F
FEB	G
MAR	H
APR	J
MAY	K
JUN	M
JUL	N
AUG	Q
SEP	U
OCT	V
NOV	X
DEC	Z

The complete ticker symbol for a futures contract will describe the commodity as a two-character code, the delivery month as a single letter and the year as a two-digit number. CCZ18, for instance, indicates a cocoa contract for delivery in December 2018.

"There are differing theories on the why of the numbers assigned to different delivery months. While the month letter codes are simply a tradition, the prevailing opinion is that letters that represent actions like bid (B) and ask (A) were removed as well as letters easily confused when spoken like C, D, and E. Add in the removal of I and L, which can be easily mistaken when written, and you are more or less at the current list. The true story doesn't really matter as long as traders and brokers in the pit know what delivery month they are talking about".

Delivery Date

A futures contract is referred to by its delivery month. The exchange where the futures contract is traded must specify the precise period during the month when delivery can be made. For some futures contracts, the delivery period is the whole month, while for others it is a specific date. The delivery months vary from contract to contract and are chosen by the exchange to meet the needs of market participants. At any given time, contracts usually trade for the closest delivery month and a number of subsequent delivery months. The exchange specifies when trading in a particular month's contract will begin. Trading generally stops a few days before the last day on which delivery can be made.

$\bullet$ All futures and forward contracts have a delivery date upon which the underlying commodity must be transferred to the contract holder if they hold the contract until maturity instead of offsetting it with an opposing contract.

First Notice Day
A First Notice Day (FND) is the day after which an investor who has purchased a futures contract may be required to take physical delivery of the contract's underlying commodity. The first notice day can vary by contract and will also depends on exchange rules.

If the first business day of the delivery month was Monday, Oct. 1, first notice day would typically fall one to three business days prior, so it could be Wednesday, Sept. 26, Thursday, Sept.27, or Friday, Sept. 28. Most investors close out their positions before first notice day because they don't want to own physical commodities. According to CME Group, only approximately 2.5% of futures contracts actually go to physical delivery.$\\$
$\bullet$ First notice day (FND) is a date specified in a futures contract after which time the owner of the contract can take physical delivery of the underlying asset.$\\$ In addition to the First Notice Day (FND), the two other key dates in a futures contract are $\bf{\text{Last Notice Day}}$, the last day the seller can deliver commodities to the buyer, and last trading day, the day after which commodities must be delivered for any futures contracts that remain open.

Physical Delivery

Derivatives>contracts such as futures or forwards can be either cash-settled or physically delivered on the expiry date of the contract. When a contract is cash-settled, the net cash position of the contract on the expiry date is transferred between the buyer and the seller.

With physical delivery, the underlying asset tied to the contract is physically delivered on a predetermined delivery date. Let’s look at an example of physical delivery. Assume two parties enter into a one-year (March 2019) Crude Oil futures contract at a futures price of $\unicode{0x0024}$58.40. Regardless of the commodity’s spot price on the settlement date, the buyer is obligated to purchase 1,000 barrels of crude oil (unit for 1 crude oil futures contract) from the seller. If the spot price on the agreed settlement day sometime in March is below $\unicode{0x0024}$58.40, the long contract holder loses and the short position gains. If the spot price is above the futures price of $\unicode{0x0024}$58.40, the long position profits, and the seller records a loss.

Last Trading Day

The last trading day is the final day that a futures contract, or other derivatives with an expiry date, may trade or be closed out before the delivery of the underlying asset or cash settlement must occur. At the end of the last trading day, the contract holder must be prepared to accept delivery of the commodity or settle in cash if the position is not closed. The same concept applies to options contracts. The last trading day is the final chance to close the position, otherwise the underlying will be delivered if applicable. If the option is worthless, then it does not need to be closed, it will simply expire.

The last trading day is the last day a derivative contract trades. Typically the last trading day is the day before the expiration date.
Expiration dates are provided in the contract specifications for a given derivative contract. Contract specifications are found on the exchange's website.
Futures contracts not closed out on the last trading day will be subject to delivery and or cash settlement.
Options contracts not closed out on the last trading day will be required to provide or take delivery of the underlying asset. Worthless contracts need not be closed. $\\$

For some derivative contracts, trading is allowed on the expiry date up to a certain time of day. In this case, the last trading day is the expiry day.

Example of the Last Trading Day in a Futures Contract:
Suppose that a speculative futures trader purchases a gold futures contract with an expiration date of August 27, 2020, which has a last trading day of August 26, 2020. If the trader doesn't sell the contract by the end of the day on August 26, the contract must be settled by delivery of the underlying asset. Most contracts also include a cash settlement option which relieves the two parties from the physical exchange of the underlying assets.

Commodity Exchanges

Some of the most popular futures and options exchanges in North America include:

Chicago Board of Trade.
Chicago Mercantile Exchange.
United States Mercantile Exchange.
United States International Monetary Financial Futures and Options Exchange.
United States Metal Exchange.
New York Mercantile Exchange.
United States Commodity Exchange

and in Asia

Shanghai Stock Exchange, China.
Tokyo Stock Exchange, Japan.
Hong Kong Stock Exchange, Hong Kong.
Shenzhen Stock Exchange, China.
Bombay Stock Exchange, India.
National Stock Exchange, India.
Korea Exchange, South Korea.

and in Europe

Euronext
London Stock Exchange
Deutsche Börse AG
NASDAQ Nordic and Baltic Exchanges
SIX Swiss Exchange

Margin Call Examples

Futures Margin Call Simulation

Interactive Tasks:

Initial Price ($/barrel):
Contract Size (barrels):
Initial Margin Rate (%):
Maintenance Margin Rate (%):
Mean Daily Return (%):
Daily Volatility (%):

Day	Futures Price ($/barrel)	P&L Amount ($)	Cumulative P&L ($)	Margin Balance ($)	Margin Call (Y/N)

Price and Margin Calls

Margin Balance and Calls

Questions:

Commodity Basis Risk

Basis Definition

A hedging strategymay involve taking an offsetting futures position opposite to one’s market position in the underlying asset. For example, a producer might sell futures short to offset a longposition in the underlying asset for example an agricultural producer. The hedge, at least in part, will realise any potential loss in the underlying asset position will be offset by profits in the hedge futures position. $\\$

The inherently imperfect correlation between cash and futures prices means there is potential for both excess gains and excess losses if the contract was unwinded so to avoid physical settlement for exampleThis risk that is specifically associated with a futures hedging strategy and is called futures curve basis risk and can be the causeof significant losses. $\\$
Basis is defined by

$$ \boxed{B_t = S_t -F(t,T)} $$

where $F(t,T)$ is the futures contract with a specific fixed expiry date $T$ seen at some time $t$. We can see in the figures below that the futures price isabove the spot price $S_t$ initially (contango) but as we approach the futures expiry the spot price is higher than the futures price (backwardation). So thecurve has quite complex dynamics as $t \rightarrow T$, that is as we approach maturity of the futures contract.

$\\[10pt]$

$\\[10pt]$So we see the futures curve above the spot rate and then later the futures curve falls below the current spot rate $S_t$. The question we are asking is if we initially put on the this contract and decided to reverse it (or unwind it) are there any P&L implications. For a simple assetthe forward and spot relation e.g. $F = S(1+rT)$ is extremely correlated so no problem will arise. Before we answer the question the termbasis has a more general context.Different types of basis risk include: $\\$

Price basis risk: The risk that occurs when the prices of the asset and its futures contract do not move with perfect correlation. This is usually do to local supply and demand disruptions.
Location basis risk: The risk that arises when the underlying asset is in a different location from the where the futures contract is traded. For example, the basis between actual crude oil sold in Houston or NewYork and the crude oil futures traded on a NYMEX futures exchange may differ.
Calendar basis risk: The selling date of the spot market position may be different from the expiry date of a futures market contract.
Product quality basis risk:When the properties or qualities of the asset are different from that of the asset as represented by the futures contract.

$\\$ Consider therisk when we open a futures position with maturity $T$ at $T_1$and close the samefutures position at $T_2$. $F(0,T)$ is the initial futures price. As mentioned earlier it is 'safer' to close the contract before the actual maturity date if you do not want to physical delivery the asset that is associated with the futures contract. One reason is that price manipulation can occur but it is mainly for procedural reasons.$\\[10pt]$

$\\[10pt]$

Commodity Consumer Risk: $\\$

A consumer is naturallyshort the asset or commodity. That is a payment is required. To hedge this futures exposure they will buy a futures contract. However the position will be closed before maturity as the consumer (perhaps) does not want to take physical delivery via the futures exchange procedures.

\begin{align}
Pay &= -S_{t_2} + (S_{t_2}-F_{(t_1,T)})-(S_{t_2}-F_{(t_2,T)}) \\
&=-S_{t_2} + F_{(t_2,T)}-F_{(t_1,T)} \\
&= -(F_{(t_1,T)}+ b(t))
\end{align}
because the basis is defined by $b(t) \equiv S_{t_2}-F_{(t_2,T)}$. Here $F_{(t_1,T)}$ is the futures price at time $t_1$ with expiry $T$ and $S_{t_2}$ is the spot price at time $t_2$. $\\$
The Consumer Risk: Will be required to pay more if the basis increases. That is the curve goes from contango (upward sloping) to backwardation (downward sloping). $\\[3pt]$

Commodity Producer: $\\$

A producer is naturally be long the asset or commodity. That is a payment will bereceived (rec).To hedge this futures exposure they will sell a futures contract.

\begin{align}
Rec &= S_{t_2} -(S_{t_2}-F_{(t_1,T)})+(S_{t_2}-F_{(t_2,T)}) \\
&= S_{t_2} + F_{(t_1,T)}-F_{(t_2,T)} \\
&= (F_{(t_1,T)}+ b(t))
\end{align}
because the basis is defined by $b(t) \equiv S_{t_2}-F_{(t_2,T)}$. Here $F_{(t_1,T)}$ is the futures price at time $t_1$ with expiry $T$ and $S_{t_2}$ is the spot price at time $t_2$. $\\$
Producer Risk:Will be receiveless if basis decreases. That is the curve goes from backwardation (downward sloping) to contango (upward sloping). $\\$

From a practical viewpoint one be must be careful, especially with agricultural commodites, to relate the production or consumer amount with the exchange definitions of the underlying asset. For example a producer may produce, 10,000 tonnes and sell as a dollar amount, yet the Wheat contract is (in the US at least) cts/bushel. So a conversion from cts/bushel to $\unicode{0x0024}$/tonne is required. The table below has some conversion factors. In the "Interactive" part we have assumed that this has been done i.e it is from the producers and consumers units. $\\[10pt]$

Commodity Conversion Units
Commodity	Prod Units	Fut Quote	Lot Size	OTC Quote	Exchange	Conversion
Wheat	Tonne	cts/bshl	5,000	$/tonne	CME	0.367437
Canola	Tonne	$/tonne	20	$/tonne	ICE	1.00
Cotton	Bales	cts/lb	50,000	$/bale	ICE	5.00
Corn	Tonne	cts/bshl	5,000	$/tonne	CME	0.39368
Soybeans	Tonne	cts/bshl	5,000	$/tonne	CME	0.367437
Soymeal	Tons	$/ton	100	$/ton	CME	1.00
Soyoil	Tonne	cts/lb	60,000	$/tonne	CME	1.00
Sugar #11	Tonne	cts/lb	112,000	$/tonne	ICE	22.0460
Coffee	Bags	cts/lb	37,500	$/bag	ICE	1.32276
Cocoa	Tonne	$/tonne	10	$/tonne	ICE	1.00

Commodity Futures Basis Risk

Spot Price at T1 (S1) Futures Price at T1 (F1) Spot Price at T2 (S2) Futures Price at T2 (F2)

Hedging with Futures

Introduction

Commodity futures hedging has its roots in the early agricultural economies where producers faced uncertainty about future prices. In 18th-century Japan, rice merchants used “rice tickets” traded at the Dojima Rice Exchange—considered one of the world’s earliest futures markets. Similarly, in 19th-century America, the Chicago Board of Trade (CBOT) was established to bring structure and transparency to grain trading. These early futures contracts allowed farmers and merchants to lock in prices for their crops or supplies, reducing the financial risk associated with fluctuating market prices. Hedging became a crucial mechanism for stabilizing income and ensuring operational continuity in volatile agricultural markets.

By the 20th century, futures hedging expanded beyond agriculture into industrial commodities such as metals and energy. The rise of standardized contracts and regulated exchanges improved market efficiency and trust. During the 1970s oil crises, energy futures became critical instruments for managing price shocks. Corporations in sectors like airlines and manufacturing began adopting futures to hedge input costs, while institutional investors entered the scene, viewing commodities as both a hedge against inflation and a diversifier from traditional asset classes. This marked a shift from hedging as a producer-driven practice to a broader financial risk management tool.

The development of financial engineering in the late 20th century further transformed futures hedging. Innovations like basis trading, spread strategies, and cross-hedging gave rise to more sophisticated approaches. The introduction of commodity indices (e.g., S\&P GSCI) allowed investors to gain broad exposure through index-linked futures, blending hedging and speculation. Meanwhile, the advent of electronic trading platforms increased liquidity and accessibility, allowing mid-sized firms and financial players to participate more actively in hedging strategies that were once limited to large producers and consumers.

In recent years, modern risk management practices have integrated commodity hedging into broader corporate treasury functions. Data analytics, real-time pricing models, and scenario analysis tools help CFOs and risk managers make dynamic decisions. Regulatory developments like Dodd-Frank in the U.S. have pushed for greater transparency and centralized clearing, especially for over-the-counter commodity derivatives. Meanwhile, the use of Environmental, Social, and Governance (ESG) criteria is influencing hedging practices, particularly in carbon-intensive industries, prompting new instruments like carbon futures and sustainability-linked hedging structures.

Consumer Hedging

Consumer hedging is often more complex than producer hedging, particularly when multiple inputs and outputs are involved. In simple cases—such as a coffee retailer that purchases unprocessed coffee, or a jeweler who buys gold to produce finished goods—the hedge typically focuses on a single commodity price. However, more sophisticated businesses, like oil refiners, face a multi-layered hedging challenge. They must hedge the price of their primary input (crude oil) while also managing price risk for their refined outputs—such as jet fuel, heating oil, or kerosene—which may be traded in both futures and over-the-counter (OTC) markets. This adds significant complexity to the hedging strategy.

Note: For an unhedged consumer they would like the future spot $S_T$ to fall as the purchase costs are less. But for an increase in the asset price it would be more expensive and would erode profits. The consumersrisk position is then$\\[10pt]$

$\\[10pt]$The exposure is -N$S_T$, where N is the quantity as the consumerneeds to pay for what it has received. To hedge this risk a long fwd contract is neededas theloss can be offset by the gains of along forward. A short spot exposure plus a long fwd contract is

\begin{align*}
Net &=-\text{N}S_T + \text{N}(S_T-F) \\
&=-NF \\
\end{align*}

where $$F is the fwd rate.Hence the consumer has payed a fixed amount which is the desired amount. As is the case with the downside of this 100% hedged strategy is that when prices fall the benefits are not passed on.

$\\[5pt]$

The payoff of the underlying risk position and the long forward isa flat line as expected.$\\[10pt]$

Recall aforward contract is an agreement to buy or sell the underlying assetat a specified future contract expiry date $T$ at an agreed rate $F_0$ which is decided at initiation of the contract. There are two parties to every futures and forward contracts- the seller of the contract, who agrees to deliver the asset at the specified time in the future, and the buyer of the contract, who agrees to pay a fixed price $F_0$ and may take delivery of the asset. For OTC's however the forward is just cash settled.$\\$

Producer Hedging

A producer might find the current market price unattractive, may wish to sell a different quantity, at a different time, or may not yet have a physical buyer lined up. In such cases, the producer can approach a bank to enter into a cash-settled forward contract. This forward contract serves as a financial overlay, allowing the producer to hedge the price risk associated with selling in the spot market at a future date—say, six months ahead. physical commodity will still be sold in the spot market when the time comes (unless it is stored). By layering on this financial hedge, the producer can effectively convert an uncertain, floating spot price into a known, fixed price—providing price certainty, as we will demonstrate next.

The producer couldthink this price is unfavourable, or wants a different volume or perhaps at a different time, or there is in fact no physical buyer.They ask a bank for a cash settled forward contract. Thus the forward contract acts as a financial overlay which can hedge the spot price risk at the time of sale, say in 6months time. The producer will still sell (unless it is stored) the produce in the spot market. By overlaying a financial hedge this floating price risk can be transformed into a fixed price as we will show. $\\$

A forward contracts allow the producerto fix an forward rate now that will act as this floating or'spot' rate at time $T$ and thus effectively removingthis futurerandom element of the underlying asset price. $\\$

Note: For an unhedged producer they would like the asset price at production time$S_T$ to increase as revenue will increase. But for adecrease in the asset price this would be unfavourable and they would receive less revenue, perhaps to a level that the production and funding costs cannot be met. The producers risk position is $\\[5pt]$

$\\[5pt]$The exposure is N$S_T$, where N is a production amount whose units may be different to the underlying forward price (e.g. wheat production may be intonnes but the asset price is in cts/bushel). If the producer is concerned with potentialprice falls then tohedge this production revenue a short fwd contract is neededas this loss can be offset with a short forward.The spot exposure $S_T$ plus a short fwd contract is

\begin{align*}
Net &=\text{N}S_T - \text{N}(S_T-F) \\
&=NF \\
\end{align*}

where $F$ is the fwd rate.Hence the producer has received a fixed amount.$\\$

$\\[5pt]$

The payoff of the underlying risk position and the short forward isa flat line as expected.$\\[15pt]$

$\\[15pt]$ It is important to see here that if the full production is hedged the net exposure to $S_T$ is zero and so any favourable price gains are negated. With derivatives elimination of risk comes at a 'cost' and here it is any upside is eliminated. $\\$

Production Risk

Most importantly firms rarely hedge 100% of production due to production risk. For example this arises in agricultural commodities in particular. If the producer fails to deliver the notional amount they would have to purchase it from the spot market and this has spot and large basis risk costs and even 'washout' clauses with the buyer of the commodity. So perhaps 30% of production may be hedged in drought prone areas like Australia but up to 75-100% hedged in Brazil where rainful is very reliable.$\\$

Note when assing the potential benefit of hedging the term opportunity cost is used. It is the difference between the guaranteed forward rate $F$, agreed to in the forward contract, and any favourable change to the asset price that the forward contract buyer would have received if they had not purchased the forward contract. The it is like a forward contract with a forward rate at today spot rate S. $\\$

Production Risk Producer One-Period Model - Income Statement with Hedge & 2D Contour Plot

Interactive Tasks:

Simple Firm: One-Period Model

Period 0: Setup & Balance Sheet

Period 1: Income Statement Inputs

Sold Forward Hedge

Period 1: Income Statement

Questions:

Hedging with Options

Option Payoffs

Forward contracts have linear payoffs and both counterparties exchange a cashflow regardless of the final spot $S_T$ at contract expiry. With an optioncontract,the holder of a call option can decide whether to exercise the payoff and for a put option the seller of the contract has the right to exercise the contract. Without this exercise right(or option) a call option is like a long fwd and a put option is like a short forward. $\\$For a call option payoff $c_T$ $\\$\begin{equation}
max(S_{T} - K,0)=
\begin{cases}
S_{T} - K, & \text{if}\ S_{T} > K \\
0, & \text{if}\ S_{T} <=K
\end{cases}
\end{equation}

where $K$ is the strike price. $\\[5pt]$

$\\[5pt]$

Aconsumer will receive the asset at$T$and is required to pay for it. The consumerwants to pay less ccyso the risk is when theasset pricerises. The risk profile is $\\[10pt]$

$\\[10pt]$

Consumers

An unhedged Consumer prefers the asset spot price to fall as less ccyis need to obtain the asset. However if the spot asset price increasesmore ccy is needed to buy the assetso the consumer will requires a hedge if $S$ rises.This suggests a long call option is required as we can see from the above call option payoff. It will profit for high spots whilst the natural position will fall. $\\$
$\underline{\mathit{\text{Hedged Consumer:}}}$ Protection when the asset price rises.$\\$
Exposure: The exposure is -amt(units) * $S_T$. To hedge this full amt a long call option contract is needed. Hence the net exposure plus the call option contract has 2 cases($\\$

$\underline{\mathbf{\text{Case1}}}:$ If option is exercised: $S_T > K$
\begin{align*}
\text{Net Position} &= -\text{amt(units)}S_T + \text{amt(units)}max(S_T - K,0) \\
&= -\text{amt(units)}K
\end{align*}Thus the importer will pay a fixed amount of ccy at a fixed asset price of $K$
$\\$
$\underline{\mathbf{\text{Case2}}}:$ If option not exercised: $S_T <= K$

\begin{align*}
\text{Net Position} &= -\text{amt(ccy2)}S_T + \text{amt(units)}max(S_T - K,0) \\
&= -\text{amt(units)}S_T
\end{align*}

In this situation the importer will pay less ccy than at the asset price of K as $S_T < K$.Recall the higher $S_T$ is unfavourable to the consumer.Suppose the asset price $S=100$ and the call strike iscould be $K=110$ for example higher than the spot to make the call option cheaper.Then the effects described above result in $\\[10pt]$

Producers

For a put option the seller of the contract has the right to exercise the contract. Without this exercice right(or option) a put option is like a short forward.Options are useful for hedgers as they can be used to set a floor on a receivedpayment (i.e.a miminum price received).
The put option payoff $p_T$is
\begin{equation}
max(K-S_{T},0)=
\begin{cases}
K-S_{T}, & \text{if}\ S_{T} <= K \\
0, & \text{if}\ S_{T} >K
\end{cases}
\end{equation}

where $K$ is the strike price.

Anproducerreceives a for ccy at time $T$. Therisk is receiving less for ccy at time$T$ as the exporterreceives less dom ccy . The risk position is $\\[10pt]$

$\underline{\mathit{\text{Unhedged Producer:}}}$ prefers the asset spot price to rise as more ccy will be received forthe asset. However if the spot asset price decreases less ccy is received for the assetso the producer will requires a hedge if $S$ falls.This suggests a long put option is required as we can see from the above put option payoffs. It will profit for low spots whilst the natural position will fall.
$\underline{\mathit{\text{Hedged Producer:}}}$ Protection when the asset price falls.$\\$
Exposure: The exposure isamt(units) * $S_T$. To hedge this full amt a long put option contract is needed. Hence the net exposure plus the put option contract has 2 cases($\\$

$\underline{\mathbf{\text{Case1}}}:$ If the put option is exercised: $S_T < K$
\begin{align*}
\text{Net Position} &= \text{amt(units)}S_T + \text{amt(units)}max(K - S_T,0) \\
&= \text{amt(units)}K
\end{align*}

Thus the producer will receivea fixed amount of ccy at a fixed asset price of $K$
$\\$
$\underline{\mathbf{\text{Case2}}}:$ If option not exercised: $S_T > K$

\begin{align*}
\text{Net Position} &= \text{amt(ccy2)}S_T + \text{amt(units)}max(K - S_T,0) \\
&= \text{amt(units)}S_T
\end{align*}

In this situation the producer will receive more dollars than at the spot price of $K$ as $S_T >K$.Recall the lower $S_T$ is unfavourable to the producer.Suppose the asset price $S=100$ and the put strike may be $K=85 $ is typically lower than spot to make the option premium cheaper.Then the combinationdescribed above result in$\\[10pt]$

$\\[10pt]$

Finally note the the underlying position of the producer has the payoff of a long asset (a straight line from left to right). That is as the asset price increases as $S_T$ increases, which is desirable. We would expect then that with a put option when combined with this 'natural' position would be protected. $\\[5pt]$

Discusssion

Let is reconsider our wheat producer example where we considered just futures hedging, that is the use of linear products. When a producer buys a put option for protection, especially one with a low strike price that becomes valuable only when prices fall significantly, the market often prices that option with a higher implied volatility. This higher implied volatility reflects a risk premium demanded by the speculators or option sellers. Here's how and why that risk premium—or "skew"—manifests:

Protection Against Extreme Downside:
- Producer's Perspective:
  A low-strike put becomes valuable when prices drop to levels that could severely impact a producer’s revenue. Essentially, the producer is buying insurance against rare but disastrous outcomes.
- Speculator's Perspective:
  The counterparty selling that put is exposed to the risk of having to pay out a large amount if a significant downward move occurs. This extreme downside risk is not common but can be very costly when it happens.
Risk Premium for Tail Risk:
- Tail Risk Explained:
  Financial returns often exhibit “fat tails,” meaning extreme outcomes (such as very low prices) occur more frequently than a normal distribution would predict.
- Extra Compensation:
  Because the risk of these extreme moves is higher than what standard models (like Black-Scholes with constant volatility) would suggest, speculators require extra compensation. This extra compensation is the risk premium for bearing the possibility of a rare, but severe, adverse event.
Manifestation as a Volatility Skew:
- Higher Implied Volatility:
  In options pricing, a higher option price (for the same strike and expiration) can be equivalently represented by a higher implied volatility.
- Skew Effect:
  When you observe that lower-strike put options (which kick in during extreme downturns) are priced with higher implied volatilities, that’s the market’s way of embedding the extra risk premium. The volatility skew is a graphical representation of this phenomenon—implied volatilities are higher for options that protect against the worst outcomes.
Market Dynamics and Demand for Insurance:
- Asymmetric Demand:
  Producers (or other risk-averse market participants) are especially keen to protect against downside risk. This strong demand for insurance against rare but extreme price falls drives up the price of these put options.
- Speculators’ Compensation:
  Knowing they are taking on the risk of having to pay out in extreme market conditions, speculators adjust the price (via a higher implied volatility) so that, on average, they are compensated for this additional risk.

When a producer buys a put option, particularly at a low strike price, the option's higher price (or equivalently, the higher implied volatility) reflects a risk premium. This premium compensates the speculator for taking on the tail risk—the chance that prices will fall to levels where the payout on the option is substantial. This additional cost is seen in the volatility skew: lower-strike puts are priced with higher implied volatilities because the speculator is essentially demanding extra compensation for the potential of extreme downside moves that are more damaging to the producer.

Examples and Calculator

Option structures, which are typically based on European-style exercise options, involve the simultaneous combination of multiple options and forwards transactions, or "legs." These structures are designed to help achieve specific trading views or investment goals. In an option structure, some options are bought (going long) and others are sold (going short). The long options require a premium to be paid, whereas the short options generate a premium. The combination of bought and sold options is referred to as an option structure, which often has a zero cost or premium upfront when the premiums of the bought and sold options offset each other.

For example:

Long options (buying options): When an investor buys an option, they are essentially purchasing the right, but not the obligation, to buy or sell an underlying asset at a predetermined price (strike price) before or at a specific date (expiration date). Buying a call option gives the investor the right to buy the asset, while buying a put option gives the investor the right to sell the asset. Purchasing an option requires the payment of a premium, which is the cost of obtaining the option contract.
Short options (selling options): When an investor sells an option, they are taking on the obligation to buy or sell the underlying asset at the strike price if the option is exercised by the option holder. Selling a call option obligates the investor to sell the asset, while selling a put option obligates the investor to buy the asset. Selling options generates a premium, which is the income received from selling the option contract.
Combining bought and sold options: An option structure combines multiple long and short options to create a more complex strategy tailored to a specific trading view or investment goal. The combination can involve various option types, such as calls and puts, with different strike prices and expiration dates. This combination is designed to achieve a particular risk-return profile, allowing the investor to manage their risk exposure and profit potential more effectively.
Zero-cost or premium upfront: In many option structures, the premiums received from selling options offset the premiums paid for buying options. This results in a zero-cost or premium upfront strategy, where the investor does not need to make an initial net payment to establish the position. This can be an attractive feature for investors seeking to minimize their upfront costs while still benefiting from the potential gains offered by the option structure.

Examples of option structures include risk reversals, collars, and spreads, which are designed to provide specific risk-return profiles depending on the investor's market view and objectives. By combining bought and sold options, investors can create tailored strategies that help them manage risk and achieve their investment goals with minimal upfront costs.

Combinations of options and forwards allow investors and 'hedgers' to create strategies based on their market outlook. These strategies can be classified into four main categories: bullish, bearish, neutral (or non-directional), and volatility-based. Let's take a closer look at each of these categories and the strategies involved. The asset price at maturity $T$ is denoted by($S_T$) and the strike of the options are $K$

Bullish strategies: These are employed when a trader expects the underlying asset's price to increase. Call options and long forwards can be used to create bullish strategies.
- Call options give the holder the right, but not the obligation, to buy an asset at a specified price (strike price) before a specific expiration date. If the asset's price rises above the strike price, the investor can exercise the option and buy the asset at the lower price, making a profit.
- Long forwards involve agreeing to buy an asset at a specific future date and price. If the asset's price increases by the time the contract expires, the investor can buy the asset at the agreed-upon price, which is lower than the market price, thus making a profit.
Bearish strategies: These are employed when a trader expects the underlying asset's price to decrease. Put options and short forwards can be used to create bearish strategies.
- Put options give the holder the right, but not the obligation, to sell an asset at a specified price before a specific expiration date. If the asset's price falls below the strike price, the investor can exercise the option and sell the asset at the higher price, making a profit.
- Short forwards involve agreeing to sell an asset at a specific future date and price. If the asset's price decreases by the time the contract expires, the investor can sell the asset at the agreed-upon price, which is higher than the market price, thus making a profit.
Neutral or non-directional strategies: These strategies are employed when a trader has no strong conviction about the direction of the underlying asset's price movement. They aim to profit from the passage of time or the changes in the asset's implied volatility. Examples of such strategies include iron condors, butterflies, and calendar spreads.
Volatility-based strategies: These strategies involve trading based on the expected level of price movement in the underlying asset, regardless of the direction. They can be further categorized into:
- Bullish on volatility: This involves anticipating large price movements, regardless of the direction. Straddles and strangles are examples of such strategies. These involve buying both call and put options with the same or different strike prices ($K$), respectively, and profiting from large price movements in either direction.
- Bearish on volatility: This involves anticipating small or minimal price movements in the underlying asset. Strategies like iron condors and butterflies can be used, which involve selling options with higher premiums and buying options with lower premiums, hoping the options expire worthless and the investor keeps the premium difference.

Some of the building blocks of common strategies are:

	Components	Market View
Long call	Call at strike price K	The profit increases as the market rises. The break-even point will be the options strike price plus the premium paid for the option
Long Put	Put at strike price K	The profit increases as the market falls. The break-even point will be the options strike price minus the premium paid for the option
Covered Calls	Buy underlying shares and Sell 1 Call of higher strike price.	Max profit will occur if the price of the stock is at or above the call strike at expiration date
Protective Put	Buy stock and buy 1 Put of lower strike price.	It is a hedging strategy to protect the portfolio against a market fall.
Bull Call Spread	Buy 1 Call at $K_1$ and Sell 1 Call of higher strike $K_2$	Profit limited to between the strikes net of premium. Moderately bullish about prices
Bull Put Spread	Buy 1 Put at $K_1$ and Sell 1 Put of higher strike $K_2$.	Moderately bullish about prices
Call Back Spread	Sell 1 Call at $K_1$ and Buy 2 Calls at higher $K_2$	Bullish up move
Bear Call Spread	Sell 1 Call at strike $K_1$ and Buy 1 Call of higher strike $K_2$	Expect downtrend but moderately bearish
Bear Put Spread	Buy 1 Put of strike $K_2$ and Sell 1 Put of lower strike $K_1$	Downward to an expected resistance line
Short strangle	Sell 1 Call of higher strike $K_2$ and Sell 1 Put of lower strike $K_1$	Stock in a sideway range and low volatility expected
Collar Strategy	Buy underlying shares S , Buy 1 Put of lower strike $K_1$ and Sell a Call of higher strike $K_2$	To protect a stock in a bullish environment
Long Butterfly	Buy 1 Call at $K_1$ and Sell 2 Calls at $K_2$ and Buy 1 Call at $K_3$. or Buy 1 Put at $K_1$ and Sell 2 Puts at $K_2$ and Buy 1 Put at $K_3$.	Small price range around the centre strike K3 is expected
Long Straddle	Buy 1 Call at K and Buy 1 Put at K	Large price move in either direction is expected

These common payoff's look like

Option structures are often designed to be zero-cost to minimize the initial capital outlay for the investor while maintaining the potential to profit from their market outlook. A zero-cost option structure is created by combining the sale (writing) of options with the purchase of other options, using the premium income received from the sold options to offset the premium expense of the purchased options.

It is quite important to realise that many of these structures alter the standard long or short forward payoff we saw in the previous section. This occurs predominantly above and below the forward price ($F$), effectively a strike $K=F$. Thus the structuring will involve options that are typically in or out of the money.

For example: The bear put spread above the forward rate ($F$)would be between $K_1$ and $K_2$. So the long put at the higher strike $K_2$ is in-the-money so would cost more. The short put at the lower strike is out-of-the money so to buy it would be cheaper.

There are several reasons why investors may prefer zero-cost option structures:

Limited capital outlay: By designing a zero-cost structure, the investor can enter a position without having to put up a significant amount of capital upfront. This can be an attractive feature for traders who want to limit their initial investment or who have limited capital available for trading.
Risk management: A zero-cost option structure can help limit the potential loss in a trade. Since the net cost of the strategy is close to zero, the investor's maximum loss is typically limited to transaction costs, such as commissions and fees, unless the options involved have margin requirements.
Flexibility: Zero-cost option structures offer investors the flexibility to create customized payoffs and risk profiles based on their market views and risk tolerance. By adjusting the strike prices and expiration dates of the options involved, investors can tailor their strategies to suit their unique needs and expectations.
Leveraging potential gains: With a zero-cost structure, investors can potentially achieve significant profits without a large initial investment. The use of options provides inherent leverage, allowing investors to control a larger amount of the underlying asset with a smaller amount of capital. This can result in sizable gains if the market moves in the anticipated direction.

Zero-cost option structures are not without risks. The potential for losses still exists, particularly if the market moves against the investor's expectations. Additionally, transaction costs, such as commissions and bid-ask spreads, can impact the profitability of these strategies.

It is important to keep track of the costs of the option 'structure'. This helps determine the breakeven point. That is what is the minimum or maximum spot value that the P&L, net of theoption premiums, becomes positive. That is a profit is created in the payoff region at the option maturity ($T$). For the basic call and put options in the above diagram this is quite easy as there is one strike $(K)$.

A trade’s breakeven point is where the trade does not make or lose money at expiration $T$.
Depending on the trade strategy, a trade could have one or multiple breakeven points.
A long call’s breakeven point is the strike price - premium paid.
A long put’s breakeven point is the strike price – premium paid.
A short call’s breakeven point is the strike price + premium received
A short put’s breakeven point is the strike price + premium received.

Here we see that there are different profit breakeven points. Consider the long Straddle.

Given the costs for the long call $c_1$ and short put $p_1$ what are $S_1$ and $S_2$ that is spot prices when the options mature $(S_T)$ that makes a positive return.

Region1:

The call has expired worthless as it required $(S_T >K_1)$ to be positive. So there is just a put option left. We require

$$ (K_1 - S_1) -(c_1+p_1) \gt 0 $$

the put payoff is just $(K-S_T)$ if exercised. So then

$$ S_1 \ltK_1 -(c_1+p_1) $$

Region2:

The put has expired worthless as it required $(S_T \le K_1)$ to be positive. So there is just a calloptionleft. We require

$$ (S_2 - K_2) -(c_1+p_1) \gt 0 $$

The put payoff is just $(K-S_T)$ if exercised. So then

$$ S_2\gtK_2+(c_1+p_1) \gt 0 $$

Eliminating risk through the use of derivatives, or taking on speculative risk can be costly. This cost comes in the form of fees, premiums, or spreads charged by financial institutions, such as banks or brokers, when facilitating or creating derivative contracts. The pricing of risk management products can vary significantly depending on the complexity of the derivative and the risk profile of the underlying asset.

When using a derivative product for hedging or speculation, it is essential to understand the nature of the risks involved and the effectiveness of the derivative instrument in mitigating or taking on those risks. Several questions can be asked.

What risk have I eliminated or acquired?

When utilizing a derivative for hedging, the goal is to offset an existing risk in your portfolio. For instance, if you have a long position in a commodity, you may use a futures contract to lock in the current price, effectively eliminating the risk of a decline in the asset's value. On the other hand, when speculating, you're intentionally acquiring risk in the expectation of a potential profit. It is crucial to identify the specific risks you are mitigating or assuming to determine whether the chosen derivative is suitable for your risk management or speculative strategy.

What risk remains?

Even after entering into a derivative contract, certain risks may still persist. Some examples of residual risks include:

Basis risk: This refers to the risk that the price of the derivative and the underlying asset may not move in perfect correlation. This can lead to an imperfect hedge or unexpected losses in speculative positions.
Counterparty risk: This is the risk that the other party involved in the derivative contract may default on their obligations. While central clearinghouses have helped mitigate this risk, it is still a consideration, especially for over-the-counter (OTC) derivatives.
Liquidity risk: This arises when you cannot easily exit your derivative position due to a lack of market participants or trading volume. In such cases, you may be unable to close out the position at the desired price or within the desired timeframe.

Is the price of the derivative fair?

Determining the fair price of a derivative is essential for both hedging and speculative purposes. A fair price ensures that you are not overpaying for risk protection or underestimating the potential gains from a speculative position. To assess whether the price of a derivative is fair, consider the following factors:

Market conditions: Market supply and demand dynamics can impact the pricing of derivatives. High demand for a specific derivative may drive up its price, while low demand could lead to a discount.
Pricing models: Various pricing models, such as the Black-Scholes model for options or the interest rate parity model for currency forwards, can help estimate the fair value of a derivative instrument. Comparing the market price to the model's output can provide insights into whether the derivative is fairly priced.
Implied volatility: For options, implied volatility is a crucial factor in determining their price. Comparing the implied volatility of the option to prices sometimes obtained on the exchangescan givea sense of whether the option is fairly priced.

These considerations should be taken into account when different risk profiles can be engineered using combinations of options or forwards.

Black-Scholes Calculator with Payoff Diagrams

Pricing Option Structures

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