Table of Contents
Dedication
Title Page
Copyright Page
Foreword
Preface
Acknowledgements
Chapter 1 - Fundamentals of Commodity Spot and Futures Markets: Instruments, ...
1.1 THE IMPORTANCE OF COMMODITY SPOT TRADING
1.2 FORWARD AND FUTURES CONTRACTS
1.3 THE ACTORS IN FUTURES MARKETS
1.4 THE STRUCTURE OF FUTURES MARKETS
1.5 SHIPPING AND FREIGHT: SPOT AND FORWARD MARKETS
1.6 VOLUME, LIQUIDITY AND OPEN INTEREST IN FUTURES MARKETS
Chapter 2 - Equilibrium Relationships between Spot Prices and Forward Prices
2.1 PRICE DISCOVERY IN FUTURES MARKETS
2.2 THEORY OF STORAGE, INVENTORY AND CONVENIENCE YIELD
2.3 SCARCITY, RESERVES AND PRICE VOLATILITY
2.4 FUTURES PRICES AND EXPECTATIONS OF FUTURE SPOT PRICES
2.5 SPOT-FORWARD RELATIONSHIP IN COMMODITY MARKETS UNDER NO-ARBITRAGE
2.6 PRICE OF A FUTURES CONTRACT AND MARKET VALUE OF A FUTURES POSITION
2.7 RELATIONSHIP BETWEEN FORWARD AND FUTURES PRICES
2.8 THE BENEFITS OF INDEXES IN COMMODITY MARKETS
Chapter 3 - Stochastic Modeling of Commodity Price Processes
3.1 RANDOMNESS AND COMMODITY PRICES
3.2 THE DISTRIBUTION OF COMMODITY PRICES AND THEIR FIRST FOUR MOMENTS
3.3 THE GEOMETRIC BROWNIAN MOTION AS A CENTRAL MODEL IN FINANCE
3.4 MEAN-REVERSION IN FINANCIAL MODELING: FROM INTEREST RATES TO COMMODITIES
3.5 INTRODUCING STOCHASTIC VOLATILITY AND JUMPS IN PRICE TRAJECTORIES
3.6 STATE VARIABLE MODELS FOR COMMODITY PRICES
3.7 COMMODITY FORWARD CURVE DYNAMICS
Chapter 4 - Plain-vanilla Option Pricing and Hedging: From Stocks to Commodities
4.1 GENERAL DEFINITIONS
4.2 CLASSICAL STRATEGIES INVOLVING EUROPEAN CALLS AND PUTS
4.3 PUT-CALL PARITY
4.4 VALUATION OF EUROPEAN CALLS: THE BLACK-SCHOLES FORMULA AND THE GREEKS
4.5 MERTON (1973) FORMULA AND ITS APPLICATION TO OPTIONS ON COMMODITY SPOT PRICES
4.6 OPTIONS ON COMMODITY SPOT PRICES
4.7 OPTIONS ON COMMODITY FUTURES AND THE BLACK (1976) FORMULA
Chapter 5 - Risk-neutral Valuation of Plain-vanilla Options
5.1 SECOND PROOF OF THE BLACK-SCHOLES-MERTON FORMULA
5.2 RISK-NEUTRAL DYNAMICS OF COMMODITY PRICES
5.3 COMMODITY FUTURES DYNAMICS UNDER THE PRICING MEASURE
5.4 IMPLIED VOLATILITY IN EQUITY OPTIONS AND LEVERAGE EFFECT
5.5 IMPLIED VOLATILITY IN ENERGY OPTION PRICES AND INVERSE LEVERAGE EFFECT
5.6 BINOMIAL TREES AND OPTION PRICING
5.7 INTRODUCING STOCHASTIC INTEREST RATES IN THE VALUATION OF COMMODITY OPTIONS
Chapter 6 - Monte Carlo Simulations and Analytical Formulae for Asian, Barrier ...
6.1 MONTE CARLO METHODS FOR EUROPEAN OPTIONS
6.2 ASIAN (ARITHMETIC AVERAGE) OPTIONS AS KEY INSTRUMENTS IN COMMODITY MARKETS
6.3 TRADING THE SHAPE OF THE FORWARD CURVE THROUGH FLOATING STRIKE ASIAN OPTIONS
6.4 BARRIER OPTIONS
6.5 COMMODITY QUANTO OPTIONS
Chapter 7 - Agricultural Commodity Markets
7.1 INTRODUCTION
7.2 THE GRAIN MARKETS
7.3 SOFT COMMODITIES: COFFEE, COTTON AND SUGAR
7.4 CITRUS AND ORANGE JUICE
7.5 LIVESTOCK MARKETS
7.6 TECHNICAL ANALYSIS IN AGRICULTURAL COMMODITY MARKETS
Chapter 8 - The Structure of Metal Markets and Metal Prices
8.1 INTRODUCTION
8.2 ABOUT METALS
8.3 OVERVIEW OF METAL MARKETS AND THEIR OPERATION
8.4 CHARACTERIZING GENERAL PRICE MOVEMENTS
8.5 CHARACTERIZING METAL PRICE MOVEMENTS
8.6 CONCLUSION
Chapter 9 - The Oil Market as a World Market
9.1 WHY OIL IS TRADED AND ITS RELATIONSHIP WITH WORLDWIDE ENERGY PRICES
9.2 CRUDE OIL MARKETS
9.3 REFINED PRODUCTS MARKETS
9.4 CONCLUSION
Chapter 10 - The Gas Market as the Energy Market of the Next Decades
10.1 THE WORLD GAS OUTLOOK
10.2 THE GAS-PRODUCING COUNTRIES
10.3 GAS SPOT MARKETS
10.4 NATURAL GAS FUTURES AND OPTIONS
10.5 THE GROWING INTEREST IN LNG
Chapter 11 - Spot and Forward Electricity Markets
11.1 INTRODUCTION
11.2 STRUCTURE OF THE ELECTRICITY INDUSTRY: FROM VERTICALLY INTEGRATED ...
11.3 SPOT POWER MARKETS AND ISSUES IN MARKET DESIGN
11.4 THE ADJUSTMENT MARKET AND RESERVES CAPACITY
11.5 ELECTRICITY DERIVATIVES MARKETS
11.6 MODELING ELECTRICITY SPOT PRICES: FROM MEAN-REVERSION AND JUMP-DIFFUSION ...
Chapter 12 - Commodity Swaptions, Swing Contracts and Real Options in the ...
12.1 COMMODITY SWAP AND SWAPTIONS
12.2 EXCHANGE OPTIONS
12.3 COMMODITY SPREAD OPTIONS
12.4 OPTIONS INVOLVING OPTIMAL STRATEGIES: AMERICAN, SWING AND TAKE-OR-PAY CONTRACTS
12.5 DISCOUNTED CASH FLOWS VERSUS REAL OPTIONS FOR THE VALUATION OF PHYSICAL ...
12.6 VALUATION OF A GAS STORAGE FACILITY
Chapter 13 - Coal, Emissions and Weather
13.1 THE COAL MARKET
13.2 EMISSIONS
13.3 WEATHER AND COMMODITY MARKETS
Chapter 14 - Commodities as a New Asset Class
14.1 INTRODUCTION
14.2 THE DIFFERENT WAYS OF INVESTING IN COMMODITIES
14.3 COMMODITY INDEXES AND COMMODITY-RELATED FUNDS
14.4 CONCLUSION
Appendix - Glossary
References
Index
For other titles in the Wiley Finance Series
please see www.wiley.com/finance
To Arnaud, Laure, Nathanael and Don
To the memory of my parents
Foreword
NASSIM NICHOLAS TALEB
It is a great honor to find myself writing this foreword for my thesis director’s book - although once someone’s student always her student, it feels awkward to comment on one’s supervisor’s work. I was also pleased to find myself among its first readers, and benefit from its contents, as this work contains the first scientific compendium ever written on the intricacies linked to the physical nature of commodities.
Commodity options are not just interesting; they harbor all the pathologies encountered in the practice of derivatives, to the point of perhaps teaching us how to value derivatives with a different, deeper approach. Methodologists consider that, to understand a phenomenon, there are two routes. The first consists in examining the regular, the ordinary and the well-behaved, and excluding the unusual. The other consists in examining pathologies, the abnormal cases, then closing in on the ordinary as the exception. Economists, alas, have traditionally tended to use the first method, by pushing the exceptions under the rug - while physicists and other hard scientists tend to resort to the second as a way to satisfy their curiosity about the world.
Why are commodity options the most interesting, and the least misunderstood, of all derivatives? And why are they the exception that would teach us about derivatives? I will attempt here to make a short list and show how we can generalize into the wrinkles of all options, including the generally perceived theory-friendly financial ones.
First, the temporal dimension. The action of borrowing and lending is hardly predictable in commodities. They are heavily grounded in their physical nature. We have been taught that securities are derived by arbitrage arguments that allow us to seamlessly borrow and lend, in order to move the asset and liability across the temporal dimension. This makes the passage from the spot to the forward (or future) seamless, smooth and direct. In the arbitrage relationship, the forward equals the spot times some function of the differential between the yield r1 and the cost of carry r2. Accordingly, the forward contract is a mere extension of the spot, with stochasticity entering on occasion with one or both of the rates r1 and r2 being nondeterministic.
Now consider that you are trading in products that are not transferable into the future. Arbitrage becomes hardly possible - and, with it, the arbitrage argument. You may be dealing with a perishable commodity, like, say, an agricultural product. Storage can cause shrinkage in quantity, as with, say, electricity. The forward might not be born yet, as in the case of cattle. Forward oil may still be in the ground and might cost no carry to the producer, whereas the arbitrageur would have to bear onerous storage costs. The relationship might hold, owing to the activities of the producer, but for arbitrage reasons.
How do you deal with it? Clearly, you need to treat every expiration like a separate underlying security. And you need to be careful about any arbitrage involving physical delivery. How does it apply to the other derivatives? Consider currency options. Currencies, I was told when I started trading two decades ago, were “clean”. No worry, you just satisfy a forward obligation by buying spot and lending it, or vice versa. But every crisis, all except for one currency, the now defunct deutschmark, started behaving like commodities. They become impossible to borrow, sometimes, as was the case of the Irish punt, in 1992, commanding as high as several thousand percent interest rates. The Canadian dollar, the New Zealand and Australian currencies, all behaved unexpectedly outside the textbook. Emerging market currencies almost always behave like commodities.
Had I been trained in commodities I would not have been squeezed on the occasion; I would have considered such possibility unlikely but a present risk. And every underlying security bears that risk, with no exception: bonds become impossible to find to satisfy a delivery obligation; stocks with heavy short interest become unavailable for the borrower. The only products that seem to escape such problem are options on Futures.
The second point is the geographic limitation. While a security that you borrow is an abstract item, a mere balance sheet entry, commodities present location specificity that can make arbitrages arduous. You can own all the oil you need in Rotterdam; but, if your delivery is in New York tomorrow, you will have a problem. In electricity, shortage in one part of a continent can rarely be compensated with excess elsewhere.
How does it apply to other derivatives? Consider the “safe” currencies again. Say that you have the currencies available in a Brazilian bank but that you have an offshore delivery obligation. The bank calls you to explain that the government forced exchange controls and that delivery will not be possible. You will have an immediate need to find offshore Brazilian currencies. There have been similar pressures with pricing differentials problems with almost all currencies.
The third point is the intricacy of storage. Commodities are “heavy”, unlike financial products. If you are expecting delivery and do not line up a warehouse you will be in trouble. Environmental agencies will not even let you dump your oil in the ocean. Cows are expensive to feed.
Do we have equivalent problems with cleaner derivatives? Of course: consider bonds that may be costly to own relative to your cost of carry, particularly when you have to borrow at a prohibitive short rate to fund them.
Fourth, the meat of the problem: dynamic hedging. Clearly, it is not possible to dynamically hedge a security that you cannot short, sometimes cannot easily own and that can be severely illiquid. Transaction costs can be monstrous. Fat tails and gaps thwart the argument that an option is a redundant security because it is safely replicated with a stream of dynamic hedges. We have enough evidence of large deviations to realize that dynamic hedging is not attainable in practice.
Then how do people value options? Clearly, options trade and we still manage to price them using risk-neutral probabilities. How do we do it? We practitioners consider an option as simply the expected value of its pay-off under some probability distribution, but not necessarily using dynamic hedging arguments.
As President of the Bachelier Finance Society, Professor Geman organized an international conference in Louis Bachelier’s honor in the summer of 2000 which featured, among others, such prominent speakers as Paul Samuelson, Robert Merton, Henri McKean and Steve Ross. Reading this book, I come to realize that we have finally vindicated Louis Bachelier: Commodities are teaching us that we do not dynamically hedge.
Enjoy this impressive book and the exciting discovery of the world of commodities.
Preface
“The world is hungry for commodities”, was the headline of the April 2004 issue of a widely read economic publication. And, indeed, there is no day when daily financial newspapers do not dedicate many columns to commodity-related issues, from cotton to nickel, coffee and freight while an unprecedented rise in oil prices has inflamed all markets.
How to define a commodity? An economist would say that it is a consumption asset whose scarcity, whether in the form of exhausting underground reserves or depleted stocks, has a major impact on the world and country-specific economic development. A banker would observe that it is not a financial security, giving rise to a stream of cash flows and priced by net present value arguments. An ecologist would suggest that it is a natural good whose original integrity should be preserved. An academic would argue that, given the current volatility of all currencies, including the most established ones, a commodity is an exemplary numéraire with respect to which portfolio values should be measured. Indeed, oil-producing countries concerned with the decline of the dollar and uncertain about the long-term health of the euro recently proposed that a barrel of oil be priced against an average of the dollar and the euro (Financial Times, February 2004). A valid suggestion would be to go the other way around and suggest a barrel of oil or a million Btus of natural gas as a “universal numéraire” relative to which all currencies would be expressed (the role gold used to play decades ago).
Commodities constitute the only spot markets which have existed nearly throughout the history of humankind. Over the centuries, even millennia, the scope of commodities available for human existence has grown from essential agricultural commodities to include metals and energy. The nature of trading has evolved from barter organized on town marketplaces in the absence of any monetary vehicle, to more elaborate forward contracting between producers and merchants, then to organized Futures markets with clearing houses guaranteeing the creditworthiness of transactions. The specification of contracts has evolved from “plain-vanilla” forwards to exotic options and structured products allowing originators and intermediaries to hedge away the risks residing outside the domain of their primary expertise.
Some key properties of commodity markets contrasting them with stock and bond markets include the following:
• Commodity spot prices are defined by the intersections of supply and demand curves in a given location, as opposed to the net present value of receivable cash flows.
• Demand for commodities is generally inelastic to prices, given the indispensable nature of the good. Inventories when they exist in sufficient volumes allow a smooth balance of supply and demand over time to be created. Hence, their importance in the discussion conducted in the economic literature for decades.
• Physical transactions - which were the only ones prior to the introduction of financial trades - still have a crucial importance today. Among other virtues, they provide a reference spot price or index against which derivative transactions are financially settled.
• Supply is defined by production and inventory. But, in the case of energy commodities, underground reserves also play a role since they have an impact on long-term prices.
• Financial transactions (forwards, Futures, options) represent today a huge volume. They involve prices closely related to spot prices in particular because physical delivery is a choice that is left to the buyer. Consequently, the understanding of spot markets and their characteristics is a necessary step in the analysis of commodities and commodity derivatives.
• For most energy commodities, the balancing of supply and demand now takes place both at the regional level and at the world level. This explains the explosion of shipping and freight markets and the emergence of new trading strategies such as the rerouting of an LNG (Liquid Natural Gas) tanker to countries where gas prices exhibit a momentary spike.
• Commodities represent today a new asset class in its own right. Many institutional investors and funds are increasingly turning to it for diversification benefits and for the returns generated.
The goal of the book is to present the three fundamental groups of commodities: agriculturals, metals and energy, with a particular emphasis on the third one in the context of deregulation of gas and electricity markets worldwide. However, the importance of the first two groups should not be dismissed: today, soybean exports from the US to China are bigger than the exports of airplanes while, in the case of Brazil, soybeans represent one-third of the shipments to China. The technical discussions will systematically emphasize the differences (or similarities), with the corresponding properties of stocks and bond markets. For instance, a crucial difference between securities and commodities is the physical delivery attached to spot, forward contracts and Futures positions not closed prior to maturity and translates into good transfer, with the corresponding constraints for both parties in terms of shipping arrangements, warehousing and so forth. The famous Sugar Quay in London gets its name from the fact that buyers of forward contracts used to be called on the phone to look out of the window and contemplate the product of their sugar transaction sitting in a barge on the Thames. At the other end of the commodity spectrum, sellers of forward contracts and options on electricity learned the hard way what physical delivery means during the crisis of June 1998: the combination of a lengthy heatwave and transmission disruption drove electricity prices up to thousands of dollars in the Midwestern part of the United States, and sent to bankruptcy firms which had sold power options without fully envisioning their unique features.
Another key difference between security and commodity markets is the existence, in the latter case, of quantity risk. Investors owning stocks or bonds are only concerned by equity markets going down or interest rates going up (i.e., by the price risk attached to the instruments they are holding). Coffee producers and power generators know that their revenues are not only affected by random moves in the spot price of coffee or electricity, but also by the variability of demand due to changes in consumption, in growth development worldwide and in weather conditions.
This explains why the variety of exotic options which are now familiar in securities markets, such as Asian, exchange or spread, are the most appropriate options in commodity markets. In the latter case, moreover, contracts quasi-unknown in financial markets, such as “take or pay” or “swing”, are playing a key role since they are designed to provide a hedge against volumetric risk. These options trade today as individual financial instruments, after having been included at no cost in contracts signed for decades between gas and electricity producers and end-users. Lastly, these options naturally appear in the so-called “real options approach” to the valuation of power plants, gas storage facilities or pipelines, as will be discussed at the end of the book.
We will try to cover a variety of theoretical and practical issues related to Futures and options markets, ranging from the mechanics of Futures trading to the discussion of equilibrium relationships between Futures and options prices, on the one hand, and spot prices, on the other hand, under some equilibrium (e.g., no-arbitrage) assumption.
The guiding thread, beyond the qualitative properties and knowledge of fundamental trading rules prevailing, respectively, in agricultural, metals and commodity markets, is to try to bring together the fundamental results from economic theory, the constraints of physical delivery and the lessons learned in modern finance and option pricing. The mathematics are kept to a minimal admissible level of formalism in order not to obscure the economic message. Readers should also get some insights about “weather to buy or sell” coffee or sugar Futures contracts, looking at the climate pattern - late frost versus warm and dry weather - prevailing across Brazil in August. Or they may wisely conclude to never plan a trip to Florida without first scrutinizing the frozen Orange Juice Futures prices posted on the New York Cotton Exchange.
Acknowledgements
First and foremost, I want to express my gratitude to Sophie Lémann, my Assistant in the Finance Department at ESSEC. Her editing talent and relentless optimism have allowed this work to move forward across oceans, airports and power conferences.
Then, I would like to thank those who helped me in various ways, including Philippe van den Abeele, Omar Alami, Martine Azara, Nilgon Baykara, Carole Boussiba, Naïma Esskali, Raj Gupta, Benjamin Geman, Aymeric Khalife, Stelios Kuruvakalis, George Martin, Jean-Pierre Mateille, Alessandro Moro, Julien Mutin, Steve Ohana, Patrick Perfetti, Patrick Slama, Jean Winghart.
Last but not least, I wish to thank Etienne Amic and Chris Harris, each of whom I invited to write chapters in his domain of unique expertise, oil and metals respectively. It is my admiration for them which explains why, throughout the book, the brilliant trader is referred to as “he”, instead of the more politically correct “she”.
1
Fundamentals of Commodity Spot and Futures Markets: Instruments, Exchanges and Strategies
1.1 THE IMPORTANCE OF COMMODITY SPOT TRADING
Commodity price risk is an important element of the world physionomy at this date, as it has an impact on the economy of both developed and developing countries: in a rough approximation, one can state that the latter include most commodity producing countries, the former being originators, marketers and manufacturers. All parties are still involved in activities of spot trading with physical delivery while the formidable development of liquid derivative markets - forward, Futures contracts and options - has paved the way for risk management and optimal design of supply and demand contracts.
Every commodity is traded on a spot market. In the old days, buyers and sellers used to meet on the marketplace where transactions led to immediate delivery. In the 18th and 19th centuries, potato growers in the state of Maine started selling their crops at the time of planting in order to finance the production process. In a parallel manner, numerous forward transactions were taking place in Chicago for cereals and agricultural products and in London for metals. A need for standardization in terms of quantity, quality, delivery date emerged and led to the establishment of the New York Cotton Exchange (NYCE) in 1842 and the Chicago Board Of Trade (CBOT) in 1848. The clearing house, unique counterparty for buyers and sellers of Futures contracts was the effective signal that the Exchange was operating. As of today, some of these clearing houses are owned by independent shareholders, others are primarily owned by market participants as in the case of the London Metal Exchange (LME) and the International Petroleum Exchange (IPE). Different qualities of the same commodity may be traded on different exchanges. The most famous examples include: coffee which in its “arabica” variety is traded on the New York Coffee, Sugar and Cocoa Exchange (CSCE), while the “robusta” type is traded on the London International Financial Futures Exchange (LIFFE); and oil which is traded on the New York Mercantile Exchange (NYMEX) as Western Texas Intermediate (WTI) and on the IPE in its Brent variety.
Let us observe that the fact that any transaction on commodities may be physical (delivery of the commodity) or financial (a cash flow from one party to the other at maturity and no exchange of the underlying good) is in sharp contrast to bonds and stock markets where all trades are financial. However, physical and financial commodity markets are, as expected, strongly related. Price and volatility observed in “paper” transactions are correlated to the analogous quantities in the physical market, both because of the physical delivery that may take place at maturity of a Futures contract and the existence of spot forward relationships that will be discussed throughout the book.
Lastly, let us note that the last two decades have experienced dramatic changes in world commodity markets. Political upheavals in some countries, economic mutation, new environmental regulation, a huge rise in the consumption of commodities in countries such as China and other structural changes have contributed to increase the volatility of supply and prices. This has made hedging activities (through forwards, Futures and options) indispensable for many sectors of the economy, the airline industry in particular being an important example.
As mantioned before, we call spot trading any transaction where delivery either takes place immediately (which is rarely the case in practice) or if there is a minimum lag, due to technical constraints, between the trade and delivery. Beyond that minimal lag, the trade becomes a forward agreement between the two parties and is properly documented by a written contract which specifies, among other things, who among the buyer and seller is responsible for shipping, unloading the goods and other transportation-related issues.
Consider a standard situation where the seller is a producer (e.g., of copper) and the buyer a manufacturer: in general, they never meet and, even if they did, would rarely agree on prices, timing and so forth. Hence the existence of intermediaries who play the role of go-between, are prepared to take delivery of goods that may not resell immediately and organize the storage and shipping.
We can represent the different phases of the physical execution of a trade as:
The document that represents the ownership of the good is called a bill of lading. It is issued either by the captain of the transportation ship or by the transporter in charge. That transportation contract may eventually be traded. It can bear the label “shipped” or “to be shipped”; the latter terminology indicates that the merchandise has been embarked, leading to the qualification clean on board.
Responsibility for commercial execution
It may lie in the hands of the seller, or the buyer, or the intermediary (since, in practice, many intermediaries will play a role, in particular because of the lags in the timing of different operations).
The responsibility will take different forms:
• For the exporter, sale Free On Board (FOB).
• For the commercial intermediary, purchase FOB out of the dock or in warehouse.
• For the importer, purchase on the dock or in warehouse.
Note that the commercial responsibility may be fragmented in the course of contract execution. For instance, a manufacturer who buys metals under a FOB specification is responsible for organizing the shipping but the armator is in charge of managing the shipping and holds the corresponding risk.
Major risks in commodity spot transaction
Four major types of risk may be identified in commodity spot markets:
• Price risk, which will be discussed throughout the book and for which the first examples of hedging strategies are presented in Section 1.2.
• Transportation risk, which is described below.
• Delivery risk, which concerns the quality of the commodity that is delivered and for which there is no financial hedge that may be put in place. The only coverage is provided by a very customized contract or by a solid long-term relationship with the originator.
• Credit risk, which is present all along until the final completion of the trade.
Risk attached to the transportation of commodities
1. The first category of risks concerns the deterioration, partial or total, of goods during transportation. Two types of risks are usually recognized in this category:
e “ordinary” risks;
e “extraordinary” risks such as wars, riots and strikes.
The expeditor of the goods or the FOB buyer directly holds the transportation risk, unless they purchase an insurance contract to be covered. Different companies specialized in freight insurance (such as the famous Lloyds of London) propose various types of contracts. We need to keep in mind that transportation risk is an important one as it includes the entire community - the tanker that sank in Alaska being a sad example. If no specific insurance coverage has been purchased, the company that bears the liability must put in place some kind of self-insurance process as do some major oil companies today.
2. Cost of transportation risk: All Futures exchanges around the world quote FOB prices. Consequently, if a trade (e.g., on sugar) is settled for delivery 12 months later with the CIF price as a reference, the seller needs to hedge his position not only against a decline in sugar prices by, say, selling Futures on the New York Coffee, Cocoa and Sugar Exchange, but also against changes in the shipping cost. The latter risk will be hedged by entering into a Forward Freight Agreement (described in Section 1.5). Consequently, the two components of the CIF price will get hedged in totally different exchanges.
1.2 FORWARD AND FUTURES CONTRACTS
A forward contract may be generically described as an agreement struck at date 0 between two parties to exchange at some fixed future date a given quantity of a commodity for an amount of dollars defined at date 0. A Futures contract has the same general features as a forward contract but is transacted through a Futures exchange. The clearing house standing behind that exchange essentially takes away any credit risk from the positions of the two participants engaged in the transaction. This default risk is almost reduced to zero through margin deposits or initial margins that need to be made before entering into any contract, as well as the daily margin calls required to keep a contract alive if its market value has declined from the previous day.
Futures contracts serve many purposes. Their first role has been to facilitate the trading of various commodities as financial instruments. But they have from the start been providing a hedging vehicle against price risk: a farmer selling his crops in January through a Futures contract maturing at time T of the harvest (say, September) for a price FT(0) defined on 1 January has secured at the beginning of the year this amount of revenue. Hence, he may allocate the proceeds to be received to the acquisition of new machinery or storage facilities and, more generally, design his investment plans for the year independently of any news of corn oversupply possibly occurring over the 9-month period.
It is noticeable in many markets, ranging from agricultural commodities to electricity, that Futures contracts are used as a substitute for the spot market by hedge funds, Commodity Trading Advisors (CTAs) or any class of investors wishing to take a position in commodities, both because it takes away the physical constraints of spot trading and provides the flexibility of short and long positions, hence the choice of positive or negative exposure to a rise in prices. This will be discussed in detail in Chapter 14.
What follows describes in detail the mechanisms of forward and Futures contracts with their various characteristics as well as the way exchanges operate. The different classes of participants, the mechanism of price discovery and the crucial relationships, if they exist, between spot prices and Futures prices under some form of equilibrium assumptions are described in detail.
Forward contracts
A forward contract is an agreement signed between two parties A and B at time 0, according to which party A has the obligation of delivering at a fixed future date T an underlying asset and party B the obligation of paying at that date an amount fixed at date 0, denoted FT(0) and called the forward price for date T for the asset. Note that this price is not a price in the sense of the price of a stock, but rather a reference value in the contractual transaction. If the underlying asset is traded in a liquid market, the no-arbitrage condition between spot and forward markets at maturity implies that:
If the value at date T of the Futures contract maturing at that date was different from the spot price, an arbitrage opportunity would be realized by buying in one market and selling immediately in the other.
Keeping in mind that the buyer of the forward contract may immediately sell at maturity in the spot market at the price
ST the commodity which was delivered to him against the payment of
FT (0) dollars, the respective Profit and Loss (P&L) of party A (called long forward) and party B (called short forward) are depicted by the following graphs:
Obviously, the contract is a zero-sum game between the buyer and the seller. Note also that, by definition, both P&Ls are expressed in dollars at date T.
For practical purposes, party A represents an economic agent who wants to hedge against a possible rise in the price of the underlying asset between dates 0 and T and locks in at date 0 a purchase price equal to FT (0). Party B, conversely, fears a collapse of this price or expects to profit from a rise. The price FT(0) represents their estimation at date 0 of how much the underlying asset S will be worth at date T together with the risk premium they are willing to pay (or receive). We will come back to this discussion in Chapter 2.
Should parties A and B enter into this T maturity contract at a future date t in the interval (0; T ), the price FT(t) on which they will agree is likely to be different from FT(0) and translates the changes between dates 0 and t in the expectations perceived by the market of the commodity future spot price S(T).
Futures contracts
They are analogous to forward contracts in terms of their definition but present some key differences from them:
• They are “standardized” in terms of their characteristics (maturity, quantity of the underlying commodity, quality or variety).
• They are traded on an exchange, such as NYMEX or the IPE; hence, they carry no counterparty risk since both the buyer and the seller of the Futures deal with the clearing house of the exchange which is in principle fully trustworthy.
• They require the payment of margin deposits in order to be able to start placing orders on the exchange.
• They are marked-to-market daily and the participants have to adjust their positions: for instance, if a participant has a long position in a Futures contract acquired at the price FT(0) and if the price FT (day 1) is lower, then this participant has experienced a loss between days 0 and 1 equal to FT (day 1) -FT(0). In order to keep his position, he has to adjust it by adding at the end of day 1 a cash amount equal to his loss.
Forward and Futures prices on the same underlying asset with the same time to expiry are different because of taxes, transaction costs and other important elements, such as the impact of credit risk on the one hand and stochastic interest rates on the other hand. In practice, they remain very close to each other since the fluctuations of the underlying commodity represent the most important explanatory factor. Except when stated otherwise, we will view the two prices as the same in a first-order approximation.
We can recap the similarities and differences between the fundamental types of transactions prevailing in commodity markets as depicted in the following diagram:
1.3 THE ACTORS IN FUTURES MARKETS
Hedgers
Futures markets were originally set up to meet the needs of hedgers, namely farmers who wanted to lock in advance a fixed price for their harvests. Commodity Futures are still widely used by producers and users of commodities for hedging purposes. Suppose that the date of analysis is January and company XYZ knows that it will have to buy on 25 September (date T) of the same year one million tons of fuel. In order to hedge against the possible increase in fuel price between January and the end of September, airline company XYZ will buy (equivalently, enter a long position in) Futures contracts written on fuel, maturity September and in an amount corresponding to the necessary quantity of fuel. By doing so, the airline company has locked in at the beginning of the year the price FT(0) it will pay in September and has done so with no cash flow payment at the beginning of the year.
Another possible hedge (as we will see later) would be to buy options - again in the appropriate quantity - written on the fuel as the underlying, with maturity T and strike price k = FT(0) for example.1 In this case, the resulting cost of fuel in September for company XYZ will be either FT(0) or, strictly, less if the market spot price is very low. This alternative is strictly superior for the hedger at maturity, but at inception of the option contract in January company XYZ will have to pay the premium of the options involved in the hedge.
Returning to Futures contracts, basic risk refers to the risk remaining after the hedge has been put in place and essentially represents the difference between the Futures price - should the Futures position be closed prematurely - and the spot price. It also includes other components such as:
• The price of cleaning the local grade of the commodity into a grade deliverable in a Futures contract (or the premium for a superior grade).
• The price of transportation to or from the delivery point in the Futures contract.
• The physical cost of storage, including insurance, between the time of the harvest and the delivery date of the Futures contract.
Speculators
While hedgers want to avoid exposure to adverse movements of the price of a commodity which is part of their manufacturing process in the economy, speculators wish to get exposure to commodity price moves (i.e., take risks in order to make profits). Using the same example as before, a bank ABC which has no “natural” exposure to the price of fuel may decide to take a position either in a Futures contract on fuel or in an option written on fuel and, by doing so, will create for itself exposure to the fuel price; obviously, the nature of the position - long or short in either instrument - will be determined by the “view” that bank ABC has on the subsequent moves of the fuel price. It is in fact “betting” that this price will go up or will go down and counting on the corresponding profits the bank will generate. Unsurprisingly, commodities are becoming increasingly attractive to investors and hedge fund managers who view them as an alternative asset class allowing one to reduce the overall risk of a financial portfolio and enhance the return as well. Futures are the obvious instrument - because of their liquidity, because of the low transaction costs on the exchange, because of the absence of credit risk - to take positions reflecting an anticipation of a price rise by purchasing Futures or a decline by selling Futures. Most of the liquidity is generated by the combined activity of speculators and hedgers.
Arbitragers
Arbitragers represent a third important - but smaller in size - group of participants in futures and options markets. An arbitrage is a riskless profit realized by simultaneously entering into several transactions in two or more markets. Arbitrage opportunities are very desirable but not easy to uncover and they do not last for long. If a given instrument is underpriced, buying activity will cause the price to rise up to a value which is viewed by the market as the “fair” price and at which there will be no more excess demand.
In this book, as in the fundamental models of option pricing, the values of Futures and options contracts will be based on the assumption of no-arbitrage opportunities. Given the importance of this concept, we are going to propose several definitions of what is called in daily language “no free lunch”.
Definition 1 A portfolio
P is called an “arbitrage portfolio” if it satisfies simultaneously the following conditions:
where H is a date later than date 0.
Definition 2 A market is said to be arbitrage-free if there exists no arbitrage opportunity; in other words, for any portfolio
P:
In other words, if a portfolio requires a null investment and is riskless (there is no possible loss at the horizon H), then its terminal value at date H has to be zero. These are the various expressions of the no free lunch property: if you start with no money and take no risk, your final wealth will be zero. In the above statements, the assumption of “riskless” is crucial: if you have no money, you can always borrow from your banker and invest the proceeds in a hedge fund. Your final wealth may be quite large or very negative once you have repaid your loan, but rarely equal to zero.
Comments
For practical purposes, traders searching for arbitrage opportunities are realistically looking, in fact, for “quasi-riskless” strategies generating profits. Such a strategy should be as simple as possible and, hence, involve only spot and forward positions which have linear payoffs and P&Ls in the underlying price, making the nullification of risk possible by the resolution of a single equation in the price S of the underlying commodity. When we move to positions involving options, we will see that the convexity (or concavity) of the P&L (i.e., the gamma of the option), together with the sensitivity to volatility (i.e., the vega), make this “quasi-riskless” feature much more problematic. Hence, it is indeed in Futures markets that the fundamental concept of arbitrage finds its origin, since fungibility between the underlying commodity and the derivative is highest. This property will be lost, however, in the case of electricity because of the specificities of this commodity (see Chapter 11) and this loss is certainly a significant part of the complexity of electricity markets. It allows us at the same time to measure the value of the spot- forward relationship when it exists, even if it holds in a temporal window because of some necessary assumptions on the convenience yield, as discussed in Chapter 2.
1.4 THE STRUCTURE OF FUTURES MARKETS
While some trading of Futures contracts may be traced back centuries ago in Europe and Japan, the modern form of Futures markets appeared in the 19th century in the American midwest. In fact, over the second half of the 19th century, more than 1,600 exchanges were established across the United States, often in the vicinity of harbors or railroad crossings. Most of them are gone today and there are only six exchanges in the United States where more that 600 million Futures contracts are traded every year (mostly softs in Chicago, energy in New York). The CBOT, established in 1848, was from the start an active exchange for agricultural commodities, especially corn and wheat. It set its General Rules in 1865. Shortly after, the New York Cotton Exchange organized cotton Futures trading. Futures trading in many other agricultural commodities followed.
The Grain Futures Act in 1922 defined the regulation of Futures exchanges; the Commodity Futures Trading Act of 1974 established the Commodity Futures Trading Commission (CFTC) as the new independent regulatory commission in charge of Futures markets. In the 1970s Futures contracts on stocks, equity indexes, bonds, foreign currencies as well as Futures on options were introduced. Active financial Futures markets have been introduced in different countries worldwide, such as Japan, the UK, France, Hong Kong and so on. Lower transaction costs, increased trading volume, expanded trading hours, electronic trading and international inter-market links contribute to make the Futures markets of today an efficient globalized trading network.
The classical structure of a Futures market is represented in the diagram below:
Most Futures exchanges are incorporated as membership associations and operated for the benefit of their members who are generally engaged in their own businesses related to Futures trading. The first purpose of an exchange is to provide an organized marketplace, with uniform rules and standardized contracts. Like any corporation, a Futures exchange has shareholders, a board of directors and executive officers. An exchange may operate markets for spot commodities, options and other financial securities in addition to Futures contracts and provide other services to the public (in particular, price discovery which will be discussed in Chapter 2). An exchange funds its activities by membership dues and by transaction fees paid on the contracts traded on the exchange.
EXCHANGE MEMBERS
Although membership is limited to individuals, these individual members often act on behalf of firms, such as brokerage houses, investment banks, or commodity dealers and producers. The total number of members of an exchange is limited; memberships are available for sale on the floor of an exchange. The value of membership lies mainly in the possibility it grants for trading contracts directly on the floor of the exchange. Those members, nominees of members and other individuals who actually use floor-trading privileges are traders. Although floor brokers sometimes trade on their own accounts, their basic role is to allow the public at large to buy or sell contracts. Collectively, they meet a critical need for liquidity, namely the ability of the market to act as a reliable and efficient mechanism for quickly taking or offsetting contract positions.
Major Futures exchanges
Chicago Board of Trade
CBOT used to be exclusively dedicated to agricultural commodities. Today, it trades Futures and options on corn, soybean, soy meal, wheat, rice as well as precious metals (gold and silver). Corn, soybean and wheat are, in this order, the most traded underlyings.
Chicago Mercantile Exchange
CME is the biggest Futures exchange in the US and the second in the world. It trades pork bellies, beef, dairy products and lumber. Founded in 1898 as a non-profit entity, it rapidly became a world platform for trading Futures.
New York Mercantile Exchange
NYMEX was founded in 1872 under the name “Butter and Cheese Exchange of New York”. It merged in 1994 with the Commodity Exchange (COMEX), itself resulting from a merger in 1933 of four smaller commodity exchanges. Today, NYMEX is the biggest exchange for commodity Futures; in particular, crude oil (WTI), gas, copper, aluminum and precious metals.
Regarding energy commodities, NYMEX trades Futures and options on crude oil, natural gas, domestic fuel, unleaded gasoline and propane. Oil Futures contracts were introduced in 1983 and are the most active contracts in the world (see Tables 1.1 and 1.2).
Futures and options on gold, silver, copper and aluminium are traded on COMEX. The gold Futures contract, launched in 1974, is a world reference today.
New York Board of Trade
NYBOT regroups the two oldest commodity exchanges in New York: the Coffee, Sugar and Cocoa Exchange (CSCE) and the New York Cotton Exchange (NYCE). The first contracts on coffee, sugar and coca were respectively introduced in 1882, 1914 and 1925 on the CSCE; those on cotton and orange juice in 1870 and 1966 on the NYCE. NYBOT also controls the New York Futures Exchange (NYFE).
International Petroleum Exchange
IPE was founded in 1980 by a consortium of energy companies. The first contract, written on gas oil, was launched one year later. In June 1988, the successful Brent contract started trading and another on natural gas was quoted as of 1997.
London International Financial Futures Exchange
LIFFE was established in 1982 and started trading agricultural commodity Futures in 1996, after it merged with the London Commodity Exchange (LCE). Futures and options on cocoa, barley, robusta coffee, sugar and potatoes are traded on LIFFE.
London Metal Exchange
LME came to existence in 1877 to serve the needs created by the industrial revolution in the United Kingdom. It specializes in non-ferrous metals: aluminum (pure or alloy), copper, nickel, tin, lead and silver. LME is where metals are traded: producers trade with speculators and hedgers, e.g., a company producing copper wires and wishing to hedge its revenues against a rise in the price of copper.
Le Marché a Terme International de France
Created in 1986 and first dedicated to bond Futures, MATIF introduced commodity Futures two years later. Today Futures on corn and Futures and options on colza and wheat are traded.
It is interesting to observe that most US Futures exchanges still function today as open outcry trading. Many exchanges around the world now operate with an electronic platform, as do some divisions of the NYMEX and the whole EUREX system existing in Europe and recently established in Chicago.
More precisely, energy trading is conducted on NYMEX in open outcry from 10.05 a.m. until 2.30 p.m. After hours Futures trading is conducted via the NYMEX access Internet-based trading platform beginning at 3.15 p.m. on Mondays through Thursdays and concluding at 9.30 a.m. the following day. On Sundays, the session begins at 7 p.m.
Table 1.1 The currently most active commodity Futures exchanges in the US and worldwide