Futures contract

(Redirected from Future Contract)

In finance, a futures contract is a standardized contract between two parties to buy or sell a specified asset of standardized quantity and quality for a price agreed today (the futures price or strike price) with delivery and payment occurring at a specified future date, the delivery date. The contracts are negotiated at a futures exchange, which acts as an intermediary between the two parties. The party agreeing to buy the underlying asset in the future, the "buyer" of the contract, is said to be "long", and the party agreeing to sell the asset in the future, the "seller" of the contract, is said to be "short". The terminology reflects the expectations of the parties—the buyer hopes or expects that the asset price is going to increase, while the seller hopes or expects that it will decrease in near future.

In many cases, the underlying asset to a futures contract may not be traditional commodities at all – that is, for financial futures the underlying asset or item can be currencies, securities or financial instruments and intangible assets or referenced items such as stock indexes and interest rates.

While the futures contract specifies a trade taking place in the future, the purpose of the futures exchange institution is to act as intermediary and minimize the risk of default by either party. Thus the exchange requires both parties to put up an initial amount of cash, the margin. Additionally, since the futures price will generally change daily, the difference in the prior agreed-upon price and the daily futures price is settled daily also (variation margin). The exchange will draw money out of one party's margin account and put it into the other's so that each party has the appropriate daily loss or profit. If the margin account goes below a certain value, then a margin call is made and the account owner must replenish the margin account. This process is known as marking to market. Thus on the delivery date, the amount exchanged is not the specified price on the contract but the spot value (since any gain or loss has already been previously settled by marking to market).

A closely related contract is a forward contract. A forward is like a futures in that it specifies the exchange of goods for a specified price at a specified future date. However, a forward is not traded on an exchange and thus does not have the interim partial payments due to marking to market. Nor is the contract standardized, as on the exchange.

Unlike an option, both parties of a futures contract must fulfill the contract on the delivery date. The seller delivers the underlying asset to the buyer, or, if it is a cash-settled futures contract, then cash is transferred from the futures trader who sustained a loss to the one who made a profit. To exit the commitment prior to the settlement date, the holder of a futures position can close out its contract obligations by taking the opposite position on another futures contract on the same asset and settlement date. The difference in futures prices is then a profit or loss.

Origin

Aristotle described the story of Thales, a poor philosopher from Miletus who developed a "financial device, which involves a principle of universal application". Thales used his skill in forecasting and predicted that the olive harvest would be exceptionally good the next autumn. Confident in his prediction, he made agreements with local olive press owners to deposit his money with them to guarantee him exclusive use of their olive presses when the harvest was ready. Thales successfully negotiated low prices because the harvest was in the future and no one knew whether the harvest would be plentiful or poor and because the olive press owners were willing to hedge against the possibility of a poor yield. When the harvest time came, and many presses were wanted concurrently and suddenly, he let them out at any rate he pleased, and made a large quantity of money.[1]

The first futures exchange market was the Dōjima Rice Exchange in Japan in the 1730s, to meet the needs of samurai who—being paid in rice, and after a series of bad harvests—needed a stable conversion to coin.[2]

The Chicago Board of Trade (CBOT) listed the first ever standardized 'exchange traded' forward contracts in 1864, which were called futures contracts. This contract was based on grain trading and started a trend that saw contracts created on a number of different commodities as well as a number of futures exchanges set up in countries around the world.[3] By 1875 cotton futures were being traded in Mumbai in India and within a few years this had expanded to futures on edible oilseeds complex, raw jute and jute goods and bullion.[4]

Standardization

Futures contracts ensure their liquidity by being highly standardized, usually by specifying:

• The underlying asset or instrument. This could be anything from a barrel of crude oil to a short term interest rate.
• The type of settlement, either cash settlement or physical settlement.
• The amount and units of the underlying asset per contract. This can be the notional amount of bonds, a fixed number of barrels of oil, units of foreign currency, the notional amount of the deposit over which the short term interest rate is traded, etc.
• The currency in which the futures contract is quoted.
• The grade of the deliverable. In the case of bonds, this specifies which bonds can be delivered. In the case of physical commodities, this specifies not only the quality of the underlying goods but also the manner and location of delivery. For example, the NYMEX Light Sweet Crude Oil contract specifies the acceptable sulphur content and API specific gravity, as well as the pricing point—the location where delivery must be made.
• The delivery month.
• Other details such as the commodity tick, the minimum permissible price fluctuation.

Margin

To minimize credit risk to the exchange, traders must post a margin or a performance bond, typically 5%-15% of the contract's value.

To minimize counterparty risk to traders, trades executed on regulated futures exchanges are guaranteed by a clearing house. The clearing house becomes the buyer to each seller, and the seller to each Buyer, so that in the event of a counterparty default the clearer assumes the risk of loss. This enables traders to transact without performing due diligence on their counterparty.

Margin requirements are waived or reduced in some cases for hedgers who have physical ownership of the covered commodity or spread traders who have offsetting contracts balancing the position.

Clearing margin are financial safeguards to ensure that companies or corporations perform on their customers' open futures and options contracts. Clearing margins are distinct from customer margins that individual buyers and sellers of futures and options contracts are required to deposit with brokers.

Customer margin Within the futures industry, financial guarantees required of both buyers and sellers of futures contracts and sellers of options contracts to ensure fulfillment of contract obligations. Futures Commission Merchants are responsible for overseeing customer margin accounts. Margins are determined on the basis of market risk and contract value. Also referred to as performance bond margin.

Initial margin is the equity required to initiate a futures position. This is a type of performance bond. The maximum exposure is not limited to the amount of the initial margin, however the initial margin requirement is calculated based on the maximum estimated change in contract value within a trading day. Initial margin is set by the exchange.

If a position involves an exchange-traded product, the amount or percentage of initial margin is set by the exchange concerned.

In case of loss or if the value of the initial margin is being eroded, the broker will make a margin call in order to restore the amount of initial margin available. Often referred to as “variation margin”, margin called for this reason is usually done on a daily basis, however, in times of high volatility a broker can make a margin call or calls intra-day.

Calls for margin are usually expected to be paid and received on the same day. If not, the broker has the right to close sufficient positions to meet the amount called by way of margin. After the position is closed-out the client is liable for any resulting deficit in the client’s account.

Some U.S. exchanges also use the term “maintenance margin”, which in effect defines by how much the value of the initial margin can reduce before a margin call is made. However, most non-US brokers only use the term “initial margin” and “variation margin”.

The Initial Margin requirement is established by the Futures exchange, in contrast to other securities' Initial Margin (which is set by the Federal Reserve in the U.S. Markets).

A futures account is marked to market daily. If the margin drops below the margin maintenance requirement established by the exchange listing the futures, a margin call will be issued to bring the account back up to the required level.

Maintenance margin A set minimum margin per outstanding futures contract that a customer must maintain in his margin account.

Margin-equity ratio is a term used by speculators, representing the amount of their trading capital that is being held as margin at any particular time. The low margin requirements of futures results in substantial leverage of the investment. However, the exchanges require a minimum amount that varies depending on the contract and the trader. The broker may set the requirement higher, but may not set it lower. A trader, of course, can set it above that, if he does not want to be subject to margin calls.

Performance bond margin The amount of money deposited by both a buyer and seller of a futures contract or an options seller to ensure performance of the term of the contract. Margin in commodities is not a payment of equity or down payment on the commodity itself, but rather it is a security deposit.

Return on margin (ROM) is often used to judge performance because it represents the gain or loss compared to the exchange’s perceived risk as reflected in required margin. ROM may be calculated (realized return) / (initial margin). The Annualized ROM is equal to (ROM+1)(year/trade_duration)-1. For example if a trader earns 10% on margin in two months, that would be about 77% annualized.

Settlement - physical versus cash-settled futures

Settlement is the act of consummating the contract, and can be done in one of two ways, as specified per type of futures contract:

• Physical delivery - the amount specified of the underlying asset of the contract is delivered by the seller of the contract to the exchange, and by the exchange to the buyers of the contract. Physical delivery is common with commodities and bonds. In practice, it occurs only on a minority of contracts. Most are cancelled out by purchasing a covering position - that is, buying a contract to cancel out an earlier sale (covering a short), or selling a contract to liquidate an earlier purchase (covering a long). The Nymex crude futures contract uses this method of settlement upon expiration
• Cash settlement - a cash payment is made based on the underlying reference rate, such as a short term interest rate index such as Euribor, or the closing value of a stock market index. The parties settle by paying/receiving the loss/gain related to the contract in cash when the contract expires.[5] Cash settled futures are those that, as a practical matter, could not be settled by delivery of the referenced item - i.e. how would one deliver an index? A futures contract might also opt to settle against an index based on trade in a related spot market. ICE Brent futures use this method.

Expiry (or Expiration in the U.S.) is the time and the day that a particular delivery month of a futures contract stops trading, as well as the final settlement price for that contract. For many equity index and interest rate futures contracts (as well as for most equity options), this happens on the third Friday of certain trading months. On this day the t+1 futures contract becomes the t futures contract. For example, for most CME and CBOT contracts, at the expiration of the December contract, the March futures become the nearest contract. This is an exciting time for arbitrage desks, which try to make quick profits during the short period (perhaps 30 minutes) during which the underlying cash price and the futures price sometimes struggle to converge. At this moment the futures and the underlying assets are extremely liquid and any disparity between an index and an underlying asset is quickly traded by arbitrageurs. At this moment also, the increase in volume is caused by traders rolling over positions to the next contract or, in the case of equity index futures, purchasing underlying components of those indexes to hedge against current index positions. On the expiry date, a European equity arbitrage trading desk in London or Frankfurt will see positions expire in as many as eight major markets almost every half an hour.

Pricing

When the deliverable asset exists in plentiful supply, or may be freely created, then the price of a futures contract is determined via arbitrage arguments. This is typical for stock index futures, treasury bond futures, and futures on physical commodities when they are in supply (e.g. agricultural crops after the harvest). However, when the deliverable commodity is not in plentiful supply or when it does not yet exist - for example on crops before the harvest or on Eurodollar Futures or Federal funds rate futures (in which the supposed underlying instrument is to be created upon the delivery date) - the futures price cannot be fixed by arbitrage. In this scenario there is only one force setting the price, which is simple supply and demand for the asset in the future, as expressed by supply and demand for the futures contract.

Arbitrage arguments

Arbitrage arguments ("Rational pricing") apply when the deliverable asset exists in plentiful supply, or may be freely created. Here, the forward price represents the expected future value of the underlying discounted at the risk free rate—as any deviation from the theoretical price will afford investors a riskless profit opportunity and should be arbitraged away.

Thus, for a simple, non-dividend paying asset, the value of the future/forward, F(t), will be found by compounding the present value S(t) at time t to maturity T by the rate of risk-free return r.

$F(t) = S(t)\times (1+r)^{(T-t)}$

or, with continuous compounding

$F(t) = S(t)e^{r(T-t)} \,$

This relationship may be modified for storage costs, dividends, dividend yields, and convenience yields.

In a perfect market the relationship between futures and spot prices depends only on the above variables; in practice there are various market imperfections (transaction costs, differential borrowing and lending rates, restrictions on short selling) that prevent complete arbitrage. Thus, the futures price in fact varies within arbitrage boundaries around the theoretical price.

Pricing via expectation

When the deliverable commodity is not in plentiful supply (or when it does not yet exist) rational pricing cannot be applied, as the arbitrage mechanism is not applicable. Here the price of the futures is determined by today's supply and demand for the underlying asset in the futures.

In a deep and liquid market, supply and demand would be expected to balance out at a price which represents an unbiased expectation of the future price of the actual asset and so be given by the simple relationship.

$F(t) = E_t\left\{S(T)\right\}$

By contrast, in a shallow and illiquid market, or in a market in which large quantities of the deliverable asset have been deliberately withheld from market participants (an illegal action known as cornering the market), the market clearing price for the futures may still represent the balance between supply and demand but the relationship between this price and the expected future price of the asset can break down.

Relationship between arbitrage arguments and expectation

The expectation based relationship will also hold in a no-arbitrage setting when we take expectations with respect to the risk-neutral probability. In other words: a futures price is martingale with respect to the risk-neutral probability. With this pricing rule, a speculator is expected to break even when the futures market fairly prices the deliverable commodity.

Contango and backwardation

The situation where the price of a commodity for future delivery is higher than the spot price, or where a far future delivery price is higher than a nearer future delivery, is known as contango. The reverse, where the price of a commodity for future delivery is lower than the spot price, or where a far future delivery price is lower than a nearer future delivery, is known as backwardation.

Futures contracts and exchanges

Contracts

There are many different kinds of futures contracts, reflecting the many different kinds of "tradable" assets about which the contract may be based such as commodities, securities (such as single-stock futures), currencies or intangibles such as interest rates and indexes. For information on futures markets in specific underlying commodity markets, follow the links. For a list of tradable commodities futures contracts, see List of traded commodities. See also the futures exchange article.

Trading on commodities began in Japan in the 18th century with the trading of rice and silk, and similarly in Holland with tulip bulbs. Trading in the US began in the mid 19th century, when central grain markets were established and a marketplace was created for farmers to bring their commodities and sell them either for immediate delivery (also called spot or cash market) or for forward delivery. These forward contracts were private contracts between buyers and sellers and became the forerunner to today's exchange-traded futures contracts. Although contract trading began with traditional commodities such as grains, meat and livestock, exchange trading has expanded to include metals, energy, currency and currency indexes, equities and equity indexes, government interest rates and private interest rates.

Exchanges

Contracts on financial instruments were introduced in the 1970s by the Chicago Mercantile Exchange (CME) and these instruments became hugely successful and quickly overtook commodities futures in terms of trading volume and global accessibility to the markets. This innovation led to the introduction of many new futures exchanges worldwide, such as the London International Financial Futures Exchange in 1982 (now Euronext.liffe), Deutsche Terminbörse (now Eurex) and the Tokyo Commodity Exchange (TOCOM). Today, there are more than 90 futures and futures options exchanges worldwide trading to include: [6]

Codes

Most Futures contracts codes are four characters. The first two characters identify the contract type, the third character identifies the month and the last character is the last digit of the year.

Third (month) futures contract codes are

• January = F
• February = G
• March = H
• April = J
• May = K
• June = M
• July = N
• August = Q
• September = U
• October = V
• November = X
• December = Z

Example: CLX0 is a Crude Oil (CL), November (X) 2010 (0) contract.[7]

Futures traders are traditionally placed in one of two groups: hedgers, who have an interest in the underlying asset (which could include an intangible such as an index or interest rate) and are seeking to hedge out the risk of price changes; and speculators, who seek to make a profit by predicting market moves and opening a derivative contract related to the asset "on paper", while they have no practical use for or intent to actually take or make delivery of the underlying asset. In other words, the investor is seeking exposure to the asset in a long futures or the opposite effect via a short futures contract.

Hedgers

Hedgers typically include producers and consumers of a commodity or the owner of an asset or assets subject to certain influences such as an interest rate.

For example, in traditional commodity markets, farmers often sell futures contracts for the crops and livestock they produce to guarantee a certain price, making it easier for them to plan. Similarly, livestock producers often purchase futures to cover their feed costs, so that they can plan on a fixed cost for feed. In modern (financial) markets, "producers" of interest rate swaps or equity derivative products will use financial futures or equity index futures to reduce or remove the risk on the swap.

Those that buy or sell commodity futures need to be careful. If a company buys contracts hedging against price increases, but in fact the market price of the commodity is substantially lower at time of delivery, they could find themselves disastrously non-competitive.

Speculators

Speculators typically fall into three categories: position traders, day traders, and swing traders (swing trading), though many hybrid types and unique styles exist. With many investors pouring into the futures markets in recent years controversy has risen about whether speculators are responsible for increased volatility in commodities like oil, and experts are divided on the matter. [8]

An example that has both hedge and speculative notions involves a mutual fund or separately managed account whose investment objective is to track the performance of a stock index such as the S&P 500 stock index. The Portfolio manager often "equitizes" cash inflows in an easy and cost effective manner by investing in (opening long) S&P 500 stock index futures. This gains the portfolio exposure to the index which is consistent with the fund or account investment objective without having to buy an appropriate proportion of each of the individual 500 stocks just yet. This also preserves balanced diversification, maintains a higher degree of the percent of assets invested in the market and helps reduce tracking error in the performance of the fund/account. When it is economically feasible (an efficient amount of shares of every individual position within the fund or account can be purchased), the portfolio manager can close the contract and make purchases of each individual stock.

The social utility of futures markets is considered to be mainly in the transfer of risk, and increased liquidity between traders with different risk and time preferences, from a hedger to a speculator, for example.

Options on futures

In many cases, options are traded on futures, sometimes called simply "futures options". A put is the option to sell a futures contract, and a call is the option to buy a futures contract. For both, the option strike price is the specified futures price at which the future is traded if the option is exercised. Futures are often used since they are delta one instruments. Calls and options on futures may be priced similarly to those on traded assets by using an extension of the Black-Scholes formula, namely Black's formula for futures.

Investors can either take on the role of option seller/option writer or the option buyer. Option sellers are generally seen as taking on more risk because they are contractually obligated to take the opposite futures position if the options buyer exercises his or her right to the futures position specified in the option. The price of an option is determined by supply and demand principles and consists of the option premium, or the price paid to the option seller for offering the option and taking on risk. [9]

Futures contract regulations

All futures transactions in the United States are regulated by the Commodity Futures Trading Commission (CFTC), an independent agency of the United States government. The Commission has the right to hand out fines and other punishments for an individual or company who breaks any rules. Although by law the commission regulates all transactions, each exchange can have its own rule, and under contract can fine companies for different things or extend the fine that the CFTC hands out.

The CFTC publishes weekly reports containing details of the open interest of market participants for each market-segment that has more than 20 participants. These reports are released every Friday (including data from the previous Tuesday) and contain data on open interest split by reportable and non-reportable open interest as well as commercial and non-commercial open interest. This type of report is referred to as the 'Commitments of Traders Report', COT-Report or simply COTR.

Definition of futures contract

Following Björk[10] we give a definition of a futures contract. We describe a futures contract with delivery of item J at the time T:

• There exists in the market a quoted price F(t,T), which is known as the futures price at time t for delivery of J at time T.
• The price of entering a futures contract is equal to zero.
• During any time interval $[t,s]$, the holder receives the amount $F(s,T) - F(t,T)$. (this reflects instantaneous marking to market)
• At time T, the holder pays F(T,T) and is entitled to receive J. Note that F(T,T) should be the spot price of J at time T.

Nonconvergence

Some exchanges tolerate 'nonconvergence', the failure of futures contracts and the value of the physical commodities they represent to reach the same value on 'contract settlement' day at the designated delivery points. An example of this is the CBOT (Chicago Board of Trade) Soft Red Winter wheat (SRW) futures. SRW futures have settled more than 20¢ apart on settlement day and as much as $1.00 difference between settlement days. Only a few participants holding CBOT SRW futures contracts are qualified by the CBOT to make or receive delivery of commodities to settle futures contracts. Therefore, it's impossible for almost any individual producer to 'hedge' efficiently when relying on the final settlement of a futures contract for SRW. The trend is for the CBOT to continue to restrict those entities that can actually participate in settling commodities contracts to those that can ship or receive large quantities of railroad cars and multiple barges at a few selected sites. The Commodity Futures Trading Commission, which has oversight of the futures market in the United States, has made no comment as to why this trend is allowed to continue since economic theory and CBOT publications maintain that convergence of contracts with the price of the underlying commodity they represent is the basis of integrity for a futures market. It follows that the function of price discovery, the ability of the markets to discern the appropriate value of a commodity reflecting current conditions, is degraded in relation to the discrepancy in price and the inability of producers to enforce contracts with the commodities they represent.[11] Futures versus forwards While futures and forward contracts are both contracts to deliver an asset on a future date at a prearranged price, they are different in two main respects: • Futures are exchange-traded, while forwards are traded over-the-counter. Thus futures are standardized and face an exchange, while forwards are customized and face a non-exchange counterparty. • Futures are margined, while forwards are not. Thus futures have significantly less credit risk, and have different funding. The Futures Industry Association (FIA) estimates that 6.97 billion futures contracts were traded in the 2007, an increase of nearly 32% over the 2006 figure. Exchange versus OTC Futures are always traded on an exchange, whereas forwards always trade over-the-counter, or can simply be a signed contract between two parties. Thus: • Futures are highly standardized, being exchange-traded, whereas forwards can be unique, being over-the-counter. • In the case of physical delivery, the forward contract specifies to whom to make the delivery. The counterparty for delivery on a futures contract is chosen by the clearing house. Margining Futures are margined daily to the daily spot price of a forward with the same agreed-upon delivery price and underlying asset (based on mark to market). Forwards do not have a standard. They may transact only on the settlement date. More typical would be for the parties to agree to true up, for example, every quarter. The fact that forwards are not margined daily means that, due to movements in the price of the underlying asset, a large differential can build up between the forward's delivery price and the settlement price, and in any event, an unrealized gain (loss) can build up. Again, this differs from futures which get 'trued-up' typically daily by a comparison of the market value of the future to the collateral securing the contract to keep it in line with the brokerage margin requirements. This true-ing up occurs by the "loss" party providing additional collateral; so if the buyer of the contract incurs a drop in value, the shortfall or variation margin would typically be shored up by the investor wiring or depositing additional cash in the brokerage account. In a forward though, the spread in exchange rates is not trued up regularly but, rather, it builds up as unrealized gain (loss) depending on which side of the trade being discussed. This means that entire unrealized gain (loss) becomes realized at the time of delivery (or as what typically occurs, the time the contract is closed prior to expiration) - assuming the parties must transact at the underlying currency's spot price to facilitate receipt/delivery. The result is that forwards have higher credit risk than futures, and that funding is charged differently. In most cases involving institutional investors, the daily variation margin settlement guidelines for futures call for actual money movement only above some insignificant amount to avoid wiring back and forth small sums of cash. The threshold amount for daily futures variation margin for institutional investors is often$1,000.

The situation for forwards, however, where no daily true-up takes place in turn creates credit risk for forwards, but not so much for futures. Simply put, the risk of a forward contract is that the supplier will be unable to deliver the referenced asset, or that the buyer will be unable to pay for it on the delivery date or the date at which the opening party closes the contract.

The margining of futures eliminates much of this credit risk by forcing the holders to update daily to the price of an equivalent forward purchased that day. This means that there will usually be very little additional money due on the final day to settle the futures contract: only the final day's gain or loss, not the gain or loss over the life of the contract.

In addition, the daily futures-settlement failure risk is borne by an exchange, rather than an individual party, further limiting credit risk in futures.

Example: Consider a futures contract with a $100 price: Let's say that on day 50, a futures contract with a$100 delivery price (on the same underlying asset as the future) costs $88. On day 51, that futures contract costs$90. This means that the "mark-to-market" calculation would requires the holder of one side of the future to pay $2 on day 51 to track the changes of the forward price ("post$2 of margin"). This money goes, via margin accounts, to the holder of the other side of the future. That is, the loss party wires cash to the other party.

A forward-holder, however, may pay nothing until settlement on the final day, potentially building up a large balance; this may be reflected in the mark by an allowance for credit risk. So, except for tiny effects of convexity bias (due to earning or paying interest on margin), futures and forwards with equal delivery prices result in the same total loss or gain, but holders of futures experience that loss/gain in daily increments which track the forward's daily price changes, while the forward's spot price converges to the settlement price. Thus, while under mark to market accounting, for both assets the gain or loss accrues over the holding period; for a futures this gain or loss is realized daily, while for a forward contract the gain or loss remains unrealized until expiry.

Note that, due to the path dependence of funding, a futures contract is not, strictly speaking, a European-style derivative: the total gain or loss of the trade depends not only on the value of the underlying asset at expiry, but also on the path of prices on the way. This difference is generally quite small though.

With an exchange-traded future, the clearing house interposes itself on every trade. Thus there is no risk of counterparty default. The only risk is that the clearing house defaults (e.g. become bankrupt), which is considered very unlikely.

Notes

1. ^ Aristotle, Politics, trans. Benjamin Jowett, vol. 2, The Great Books of the Western World, book 1, chap. 11, p. 453.
2. ^ Schaede, Ulrike (September 1989). "Forwards and futures in tokugawa-period Japan:A new perspective on the Djima rice market". Journal of Banking & Finance 13 (4–5): 487–513. doi:10.1016/0378-4266(89)90028-9
3. ^ "timeline-of-achievements". CME Group. Retrieved August 5, 2010.
4. ^ Inter-Ministerial task force (chaired by Wajahat Habibullah) (May 2003). "Convergence of Securities and Commodity Markets report". Forward Markets Commission (India). Retrieved August 5, 2010.
5. ^ Cash settlement on Wikinvest
6. ^ Futures & Options Factbook. Institute for Financial Markets
7. ^ http://www.cmegroup.com/product-codes-listing/month-codes.html
8. ^ Dreibus, Tony C. Commodity Bubbles Caused by Speculators Need Intervention, UN Agency Says, Bloomberg, June 5, 2011. Accessed July 2, 2011
9. ^ CME Group CME Options on Futures: The Basics. Accessed February 8, 2011
10. ^ Björk: Arbitrage theory in continuous time, Cambridge university press, 2004
11. ^ Henriques, D Mysterious discrepancies in grain prices baffle experts, International Herald Tribune, March 23, 2008. Accessed April 12, 2008

References

• The Institute for Financial Markets (2003). Futures & Options. Washington, DC: The IFM. p. 237.
• Redhead, Keith (1997). Financial Derivatives: An Introduction to Futures, Forwards, Options and Swaps. London: Prentice-Hall. ISBN 0-13-241399-X.
• Lioui, Abraham; Poncet, Patrice (2005). Dynamic Asset Allocation with Forwards and Futures. New York: Springer. ISBN 0-387-24107-8.
• Valdez, Steven (2000). An Introduction To Global Financial Markets (3rd ed.). Basingstoke, Hampshire: Macmillan Press. ISBN 0-333-76447-1.
• Arditti, Fred D. (1996). Derivatives: A Comprehensive Resource for Options, Futures, Interest Rate Swaps, and Mortgage Securities. Boston: Harvard Business School Press. ISBN 0-87584-560-6.