A derivative instrument is a contract between two parties that specifies conditions (especially the dates, resulting values of the underlying variables, and notional amounts) under which payments are to be made between the parties.
Under US law and the laws of most other developed countries, derivatives have special legal exemptions that make them a particularly attractive legal form through which to extend credit. However, the strong creditor protections afforded to derivatives counterparties, in combination with their complexity and lack of transparency, can cause capital markets to underprice credit risk. This can contribute to credit booms, and increase systemic risks. Indeed, the use of derivatives to mask credit risk from third parties while protecting derivative counterparties contributed to the financial crisis of 2008 in the United States.
Financial reforms within the US since the financial crisis have served only to reinforce special protections for derivatives, including greater access to government guarantees, while minimizing disclosure to broader financial markets.
One of the oldest derivatives is rice futures, which have been traded on the Dojima Rice Exchange since the eighteenth century. Derivatives are broadly categorized by the relationship between the underlying asset and the derivative (such as forward, option, swap); the type of underlying asset (such as equity derivatives, foreign exchange derivatives, interest rate derivatives, commodity derivatives, or credit derivatives); the market in which they trade (such as exchange-traded or over-the-counter); and their pay-off profile.
Derivatives can be used for speculating purposes ("bets") or to hedge ("insurance"). For example, a speculator may sell deep in-the-money naked calls on a stock, expecting the stock price to plummet, but exposing himself to potentially unlimited losses. Very commonly, companies buy currency forwards in order to limit losses due to fluctuations in the exchange rate of two currencies.
Third parties can use publicly available derivative prices as educated predictions of uncertain future outcomes, for example, the likelihood that a corporation will default on its debts.
Derivatives are used by investors for the following:
- provide leverage (or gearing), such that a small movement in the underlying value can cause a large difference in the value of the derivative;
- speculate and make a profit if the value of the underlying asset moves the way they expect (e.g., moves in a given direction, stays in or out of a specified range, reaches a certain level);
- hedge or mitigate risk in the underlying, by entering into a derivative contract whose value moves in the opposite direction to their underlying position and cancels part or all of it out;
- obtain exposure to the underlying where it is not possible to trade in the underlying (e.g., weather derivatives);
- create option ability where the value of the derivative is linked to a specific condition or event (e.g. the underlying reaching a specific price level).
Derivatives allow risk related to the price of the underlying asset to be transferred from one party to another. For example, a wheat farmer and a miller could sign a futures contract to exchange a specified amount of cash for a specified amount of wheat in the future. Both parties have reduced a future risk: for the wheat farmer, the uncertainty of the price, and for the miller, the availability of wheat. However, there is still the risk that no wheat will be available because of events unspecified by the contract, such as the weather, or that one party will renege on the contract. Although a third party, called a clearing house, insures a futures contract, not all derivatives are insured against counter-party risk.
From another perspective, the farmer and the miller both reduce a risk and acquire a risk when they sign the futures contract: the farmer reduces the risk that the price of wheat will fall below the price specified in the contract and acquires the risk that the price of wheat will rise above the price specified in the contract (thereby losing additional income that he could have earned). The miller, on the other hand, acquires the risk that the price of wheat will fall below the price specified in the contract (thereby paying more in the future than he otherwise would have) and reduces the risk that the price of wheat will rise above the price specified in the contract. In this sense, one party is the insurer (risk taker) for one type of risk, and the counter-party is the insurer (risk taker) for another type of risk.
Hedging also occurs when an individual or institution buys an asset (such as a commodity, a bond that has coupon payments, a stock that pays dividends, and so on) and sells it using a futures contract. The individual or institution has access to the asset for a specified amount of time, and can then sell it in the future at a specified price according to the futures contract. Of course, this allows the individual or institution the benefit of holding the asset, while reducing the risk that the future selling price will deviate unexpectedly from the market's current assessment of the future value of the asset.
Derivatives can serve legitimate business purposes. For example, a corporation borrows a large sum of money at a specific interest rate. The rate of interest on the loan resets every six months. The corporation is concerned that the rate of interest may be much higher in six months. The corporation could buy a forward rate agreement (FRA), which is a contract to pay a fixed rate of interest six months after purchases on a notional amount of money. If the interest rate after six months is above the contract rate, the seller will pay the difference to the corporation, or FRA buyer. If the rate is lower, the corporation will pay the difference to the seller. The purchase of the FRA serves to reduce the uncertainty concerning the rate increase and stabilize earnings.
Speculation and arbitrage
Derivatives can be used to acquire risk, rather than to hedge against risk. Thus, some individuals and institutions will enter into a derivative contract to speculate on the value of the underlying asset, betting that the party seeking insurance will be wrong about the future value of the underlying asset. Speculators look to buy an asset in the future at a low price according to a derivative contract when the future market price is high, or to sell an asset in the future at a high price according to a derivative contract when the future market price is low.
Individuals and institutions may also look for arbitrage opportunities, as when the current buying price of an asset falls below the price specified in a futures contract to sell the asset.
Speculative trading in derivatives gained a great deal of notoriety in 1995 when Nick Leeson, a trader at Barings Bank, made poor and unauthorized investments in futures contracts. Through a combination of poor judgment, lack of oversight by the bank's management and regulators, and unfortunate events like the Kobe earthquake, Leeson incurred a US$1.3 billion loss that bankrupted the centuries-old institution.
OTC and exchange-traded
In broad terms, there are two groups of derivative contracts, which are distinguished by the way they are traded in the market:
- Over-the-counter (OTC) derivatives are contracts that are traded (and privately negotiated) directly between two parties, without going through an exchange or other intermediary. Products such as swaps, forward rate agreements, exotic options - and other exotic derivatives - are almost always traded in this way. The OTC derivative market is the largest market for derivatives, and is largely unregulated with respect to disclosure of information between the parties, since the OTC market is made up of banks and other highly sophisticated parties, such as hedge funds. Reporting of OTC amounts are difficult because trades can occur in private, without activity being visible on any exchange. According to the Bank for International Settlements, the total outstanding notional amount is US$708 trillion (as of June 2011). Of this total notional amount, 67% are interest rate contracts, 8% are credit default swaps (CDS), 9% are foreign exchange contracts, 2% are commodity contracts, 1% are equity contracts, and 12% are other. Because OTC derivatives are not traded on an exchange, there is no central counter-party. Therefore, they are subject to counter-party risk, like an ordinary contract, since each counter-party relies on the other to perform.
- Exchange-traded derivative contracts (ETD) are those derivatives instruments that are traded via specialized derivatives exchanges or other exchanges. A derivatives exchange is a market where individuals trade standardized contracts that have been defined by the exchange. A derivatives exchange acts as an intermediary to all related transactions, and takes initial margin from both sides of the trade to act as a guarantee. The world's largest derivatives exchanges (by number of transactions) are the Korea Exchange (which lists KOSPI Index Futures & Options), Eurex (which lists a wide range of European products such as interest rate & index products), and CME Group (made up of the 2007 merger of the Chicago Mercantile Exchange and the Chicago Board of Trade and the 2008 acquisition of the New York Mercantile Exchange). According to BIS, the combined turnover in the world's derivatives exchanges totaled USD 344 trillion during Q4 2005. Some types of derivative instruments also may trade on traditional exchanges. For instance, hybrid instruments such as convertible bonds and/or convertible preferred may be listed on stock or bond exchanges. Also, warrants (or "rights") may be listed on equity exchanges. Performance Rights, Cash xPRTs and various other instruments that essentially consist of a complex set of options bundled into a simple package are routinely listed on equity exchanges. Like other derivatives, these publicly traded derivatives provide investors access to risk/reward and volatility characteristics that, while related to an underlying commodity, nonetheless are distinctive.
Common derivative contract types
Some of the common variants of derivative contracts are as follows:
- Forwards: A tailored contract between two parties, where payment takes place at a specific time in the future at today's pre-determined price.
- Futures: are contracts to buy or sell an asset on or before a future date at a price specified today. A futures contract differs from a forward contract in that the futures contract is a standardized contract written by a clearing house that operates an exchange where the contract can be bought and sold; the forward contract is a non-standardized contract written by the parties themselves.
- Options are contracts that give the owner the right, but not the obligation, to buy (in the case of a call option) or sell (in the case of a put option) an asset. The price at which the sale takes place is known as the strike price, and is specified at the time the parties enter into the option. The option contract also specifies a maturity date. In the case of a European option, the owner has the right to require the sale to take place on (but not before) the maturity date; in the case of an American option, the owner can require the sale to take place at any time up to the maturity date. If the owner of the contract exercises this right, the counter-party has the obligation to carry out the transaction. Options are of two types: call option and put option. The buyer of a Call option has a right to buy a certain quantity of the underlying asset, at a specified price on or before a given date in the future, he however has no obligation whatsoever to carry out this right. Similarly, the buyer of a Put option has the right to sell a certain quantity of an underlying asset, at a specified price on or before a given date in the future, he however has no obligation whatsoever to carry out this right.
- Binary options are contracts that provide the owner with an all-or-nothing profit profile.
- Warrants: Apart from the commonly used short-dated options which have a maximum maturity period of 1 year, there exists certain long-dated options as well, known as Warrant (finance). These are generally traded over-the-counter.
- Swaps are contracts to exchange cash (flows) on or before a specified future date based on the underlying value of currencies exchange rates, bonds/interest rates, commodities exchange, stocks or other assets. Another term which is commonly associated to Swap is Swaption which is basically an option on the forward Swap. Similar to a Call and Put option, a Swaption is of two kinds: a receiver Swaption and a payer Swaption. While on one hand, in case of a receiver Swaption there is an option wherein you can receive fixed and pay floating, a payer swaption on the other hand is an option to pay fixed and receive floating.
Swaps can basically be categorized into two types:
- Interest Rate Swap: These basically necessitate swapping only interest associated cash flows in the same currency, between two parties.
- Currency swap: In this kind of swapping, the cash flow between the two parties includes both principal and interest. Also, the money which is being swapped is in different currency for both parties.
The overall derivatives market has five major classes of underlying asset:
Some common examples of these derivatives are the following:
Other examples of underlying exchangeables are:
Economic function of the derivative market
Some of the salient economic functions of the derivative market include:
- Prices in a structured derivative market not only replicate the discernment of the market participants about the future but also lead the prices of underlying to the professed future level. On the expiration of the derivative contract, the prices of derivatives congregate with the prices of the underlying. Therefore, derivatives are essential tools to determine both current and future prices.
- The derivatives market relocates risk from the people who prefer risk aversion to the people who have an appetite for risk.
- The intrinsic nature of derivatives market associates them to the underlying Spot market. Due to derivatives there is a considerable increase in trade volumes of the underlying Spot market. The dominant factor behind such an escalation is increased participation by additional players who would not have otherwise participated due to absence of any procedure to transfer risk.
- As supervision, reconnaissance of the activities of various participants becomes tremendously difficult in assorted markets; the establishment of an organized form of market becomes all the more imperative. Therefore, in the presence of an organized derivatives market, speculation can be controlled, resulting in a more meticulous environment.
- A significant accompanying benefit which is a consequence of derivatives trading is that it acts as a facilitator for new Entrepreneurs. The derivatives market has a history of alluring many optimistic, imaginative and well educated people with an entrepreneurial outlook, the benefits of which are colossal.
In a nutshell, there is a substantial increase in savings and investment in the long run due to augmented activities by derivative Market participant.
Total world derivatives from 1998–2007
compared to total world wealth in the year 2000
Market and arbitrage-free prices
Two common measures of value are:
- Market price, i.e., the price at which traders are willing to buy or sell the contract;
- Arbitrage-free price, meaning that no risk-free profits can be made by trading in these contracts; see rational pricing.
Determining the market price
For exchange-traded derivatives, market price is usually transparent, making it difficult to automatically broadcast prices. In particular with OTC contracts, there is no central exchange to collate and disseminate prices.
Determining the arbitrage-free price
- See List of finance topics# Derivatives pricing.
The arbitrage-free price for a derivatives contract can be complex, and there are many different variables to consider. Arbitrage-free pricing is a central topic of financial mathematics. For futures/forwards the arbitrage free price is relatively straightforward, involving the price of the underlying together with the cost of carry (income received less interest costs), although there can be complexities.
However, for options and more complex derivatives, pricing involves developing a complex pricing model: understanding the stochastic process of the price of the underlying asset is often crucial. A key equation for the theoretical valuation of options is the Black–Scholes formula, which is based on the assumption that the cash flows from a European stock option can be replicated by a continuous buying and selling strategy using only the stock. A simplified version of this valuation technique is the binomial options model.
OTC represents the biggest challenge in using models to price derivatives. Since these contracts are not publicly traded, no market price is available to validate the theoretical valuation. Most of the model's results are input-dependent (meaning the final price depends heavily on how we derive the pricing inputs). Therefore it is common that OTC derivatives are priced by Independent Agents that both counterparties involved in the deal designate upfront (when signing the contract).
Derivatives are often subject to the following criticisms:
Erroneous Analysis of Benefits
Economists and bankers claimed derivatives made markets safer. But instead, they made them [the markets] unstable.
Hidden Tail Risk
According to Raghuram Rajan, a former chief economist of the International Monetary Fund (IMF), "... it may well be that the managers of these firms [investment funds] have figured out the correlations between the various instruments they hold and believe they are hedged. Yet as Chan and others (2005) point out, the lessons of summer 1998 following the default on Russian government debt is that correlations that are zero or negative in normal times can turn overnight to one — a phenomenon they term “phase lock-in.” A hedged position can become unhedged at the worst times, inflicting substantial losses on those who mistakenly believe they are protected."
The use of derivatives can result in large losses because of the use of leverage, or borrowing. Derivatives allow investors to earn large returns from small movements in the underlying asset's price. However, investors could lose large amounts if the price of the underlying moves against them significantly. There have been several instances of massive losses in derivative markets, such as the following:
- American International Group (AIG) lost more than US$18 billion through a subsidiary over the preceding three quarters on Credit Default Swaps (CDS). The US federal government then gave the company US$85 billion in an attempt to stabilize the economy before an imminent stock market crash. It was reported that the gifting of money,which came to be known as the "Back door bailout" of America's largest trading firms, was necessary because over the next few quarters the company was likely to lose more money.
- The loss of US$7.2 Billion by Société Générale in January 2008 through mis-use of futures contracts.
- The loss of US$6.4 billion in the failed fund Amaranth Advisors, which was long natural gas in September 2006 when the price plummeted.
- The loss of US$4.6 billion in the failed fund Long-Term Capital Management in 1998.
- The loss of US$1.3 billion equivalent in oil derivatives in 1993 and 1994 by Metallgesellschaft AG.
- The loss of US$1.2 billion equivalent in equity derivatives in 1995 by Barings Bank.
- UBS AG, Switzerland’s biggest bank, suffered a $2 billion loss through unauthorized trading discovered in September, 2011.
This comes to a staggering $39.5 billion, the majority in the last decade after the Commodity Futures Modernization Act of 2000 was passed.
Counter party risk
Some derivatives (especially swaps) expose investors to counter party risk, or risk arising from the other party in a financial transaction. Different types of derivatives have different levels of counter party risk. For example, standardized stock options by law require the party at risk to have a certain amount deposited with the exchange, showing that they can pay for any losses; banks that help businesses swap variable for fixed rates on loans may do credit checks on both parties. However, in private agreements between two companies, for example, there may not be benchmarks for performing due diligence and risk analysis.
Large notional value
Derivatives typically have a large notional value. As such, there is the danger that their use could result in losses for which the investor would be unable to compensate. The possibility that this could lead to a chain reaction ensuing in an economic crisis was pointed out by famed investor Warren Buffett in Berkshire Hathaway's 2002 annual report. Buffett called them 'financial weapons of mass destruction.' The problem with derivatives is that they control an increasingly larger notional amount of assets and this may lead to distortions in the real capital and equities markets. Investors begin to look at the derivatives markets to make a decision to buy or sell securities and so what was originally meant to be a market to transfer risk now becomes a leading indicator.(See Berkshire Hathaway Annual Report for 2002)
Leverage of an economy's debt
Derivatives massively leverage the debt in an economy, making it ever more difficult for the underlying real economy to service its debt obligations, thereby curtailing real economic activity, which can cause a recession or even depression. In the view of Marriner S. Eccles, US Federal Reserve Chairman from November, 1934 to February, 1948, too high a level of debt was one of the primary causes of the Great Depression. (See Berkshire Hathaway Annual Report for 2002)
The use of derivatives also has its benefits:
- Derivatives facilitate the buying and selling of risk, and many financial professionalseconomic system. Although someone loses money while someone else gains money with a derivative, under normal circumstances, trading in derivatives should not adversely affect the economic system because it is not zero-sum in utility.
consider this to have a positive impact on the
In the context of a 2010 examination of the ICE Trust, an industry self-regulatory body, Gary Gensler, the chairman of the Commodity Futures Trading Commission which regulates most derivatives, was quoted saying that the derivatives marketplace as it functions now "adds up to higher costs to all Americans." More oversight of the banks in this market is needed, he also said. Additionally, the report said, "[t]he Department of Justice is looking into derivatives, too. The department’s antitrust unit is actively investigating 'the possibility of anticompetitive practices in the credit derivatives clearing, trading and information services industries,' according to a department spokeswoman."
Over-the-counter dealing will be less common as the 2010 Dodd-Frank Wall Street Reform Act comes into effect. The law mandated the clearing of certain swaps at registered exchanges and imposed various restrictions on derivatives. To implement Dodd-Frank, the CFTC developed new rules in at least 30 areas. The Commission determines which swaps are subject to mandatory clearing and whether a derivatives exchange is eligible to clear a certain type of swap contract.
- Bilateral netting: A legally enforceable arrangement between a bank and a counter-party that creates a single legal obligation covering all included individual contracts. This means that a bank’s obligation, in the event of the default or insolvency of one of the parties, would be the net sum of all positive and negative fair values of contracts included in the bilateral netting arrangement.
- Counterparty: The legal and financial term for the other party in a financial transaction.
- Credit derivative: A contract that transfers credit risk from a protection buyer to a credit protection seller. Credit derivative products can take many forms, such as credit default swaps, credit linked notes and total return swaps.
- Derivative: A financial contract whose value is derived from the performance of assets, interest rates, currency exchange rates, or indexes. Derivative transactions include a wide assortment of financial contracts including structured debt obligations and deposits, swaps, futures, options, caps, floors, collars, forwards and various combinations thereof.
- Exchange-traded derivative contracts: Standardized derivative contracts (e.g., futures contracts and options) that are transacted on an organized futures exchange.
- Gross negative fair value: The sum of the fair values of contracts where the bank owes money to its counter-parties, without taking into account netting. This represents the maximum losses the bank’s counter-parties would incur if the bank defaults and there is no netting of contracts, and no bank collateral was held by the counter-parties.
- Gross positive fair value: The sum total of the fair values of contracts where the bank is owed money by its counter-parties, without taking into account netting. This represents the maximum losses a bank could incur if all its counter-parties default and there is no netting of contracts, and the bank holds no counter-party collateral.
- High-risk mortgage securities: Securities where the price or expected average life is highly sensitive to interest rate changes, as determined by the U.S. Federal Financial Institutions Examination Council policy statement on high-risk mortgage securities.
- Notional amount: The nominal or face amount that is used to calculate payments made on swaps and other risk management products. This amount generally does not change hands and is thus referred to as notional.
- Over-the-counter (OTC) derivative contracts: Privately negotiated derivative contracts that are transacted off organized futures exchanges.
- Structured notes: Non-mortgage-backed debt securities, whose cash flow characteristics depend on one or more indices and / or have embedded forwards or options.
- Total risk-based capital: The sum of tier 1 plus tier 2 capital. Tier 1 capital consists of common shareholders equity, perpetual preferred shareholders equity with non-cumulative dividends, retained earnings, and minority interests in the equity accounts of consolidated subsidiaries. Tier 2 capital consists of subordinated debt, intermediate-term preferred stock, cumulative and long-term preferred stock, and a portion of a bank’s allowance for loan and lease losses.
- ^ Rubinstein, Mark (1999). Rubinstein on derivatives. Risk Books. ISBN 1-899332-53-7.
- ^ Hull, John C. (2006). Options, Futures and Other Derivatives, Sixth Edition. Prentice Hall. pp. 1.
- ^ a b c Michael Simkovic, Secret Liens and the Financial Crisis of 2008, American Bankruptcy Law Journal, Vol. 83, p. 253, 2009
- ^ Michael Simkovic, Bankruptcy Immunities, Transparency, and Capital Structure, Presentation at the World Bank, January 11, 2011
- ^ Michael Simkovic, Paving the Way for the Next Financial Crisis, Banking & Financial Services Policy Report, Vol. 29, No. 3, 2010
- ^ Kaori Suzuki and David Turner (December 10, 2005). "Sensitive politics over Japan's staple crop delays rice futures plan". The Financial Times. http://www.ft.com/cms/s/0/d9f45d80-6922-11da-bd30-0000779e2340.html. Retrieved October 23, 2010.
- ^ Michael Simkovic and Benjamin Kaminetzky, Leveraged Buyout Bankruptcies, the Problem of Hindsight Bias, and the Credit Default Swap Solution (August 29, 2010). Columbia Business Law Review, Vol. 2011, No. 1, p. 118, 2011
- ^ Shirreff, David (2004). "Derivatives and leverage". Dealing With Financial Risk. USA: The Economist. p. 23. ISBN 1-57660-162-5. http://books.google.com/books?id=mwirEO_f1DkC. Retrieved 14 September 2011.
- ^ Khullar, Sanjeev (2009). "Using Derivatives to Create Alpha". In John M. Longo. Hedge Fund Alpha: A Framework for Generating and Understanding Investment Performance. Singapore: World Scientific. p. 105. ISBN 978-981-283-465-2. http://books.google.com/books?id=uv73DVVSgAsC. Retrieved 14 September 2011.
- ^ Don M. Chance; Robert Brooks (2010). "Advanced Derivatives and Strategies". Introduction to Derivatives and Risk Management (8th ed.). Mason, Ohio: Cengage Learning. pp. 483–515. ISBN 978-0-324-60120-6. http://books.google.com/books?id=DT0nnLDMYTgC. Retrieved 14 September 2011.
- ^ Chisolm, Derivatives Demystified (Wiley 2004)
- ^ Chisolm, Derivatives Demystified (Wiley 2004) Notional sum means there is no actual principal.
- ^ News.BBC.co.uk, "How Leeson broke the bank – BBC Economy"
- ^ BIS survey: The Bank for International Settlements (BIS) semi-annual OTC [derivatives market report, for end of June 2008, shows US$683.7 trillion total notional amounts outstanding of OTC derivatives with a gross market value of US$20 trillion. See also Prior Period Regular OTC Derivatives Market Statistics.
- ^ Hull, J.C. (2009). Options, futures, and other derivatives . Upper Saddle River, NJ : Pearson/Prentice Hall, c2009
- ^ Futures and Options Week: According to figures published in F&O Week 10 October 2005. See also FOW Website.
- ^ "Financial Markets: A Beginner's Module". http://www.nseindia.com/education/content/module_ncfm.htm.
- ^ "Biz.Yahoo.com". Biz.Yahoo.com. 2010-08-23. http://biz.yahoo.com/c/e.html. Retrieved 2010-08-29.
- ^ Canter, Michael S.; Cole, Joseph B.; Sandor, Richard L. (1996). "Insurance Derivatives – A New Asset Class for the Capital Markets and a New Hedging Tool for the Insurance Industry". Journal of Derivatives 4 (2): 89–104. DOI:10.3905/jod.1996.407966.
- ^ FOW.com, Emissions derivatives, 1 December 2005
- ^ "Currency Derivatives: A Beginner's Module". http://www.nseindia.com/education/content/module_ncfm.htm.
- ^ "Bis.org". Bis.org. 2010-05-07. http://www.bis.org/statistics/derstats.htm. Retrieved 2010-08-29.
- ^ "Launch of the WIDER study on The World Distribution of Household Wealth: 5 December 2006". http://www.wider.unu.edu/events/past-events/2006-events/en_GB/05-12-2006/. Retrieved 9 June 2009.
- ^ Boumlouka, Makrem (2009),"Alternatives in OTC Pricing", Hedge Funds Review, 10-30-2009. http://www.hedgefundsreview.com/hedge-funds-review/news/1560286/otc-pricing-deal-struck-fitch-solutions-pricing-partners
- ^ Ferguson, Charles (Director) (May 16, 2010). Inside Job (Television Documentary (DVD)). Sony Pictures Classics. Event occurs at 22:58. http://www.imdb.com/title/tt1645089/.
- ^ Raghuram G. Rajan (September 2006). "Has Financial Development Made the World Riskier?". EUROPEAN FINANCIAL MANAGEMENT (EUROPEAN FINANCIAL MANAGEMENT) 12 (4): 499–533. DOI:10.1111/j.1468-036X.2006.00330.x. http://ssrn.com/abstract=923683. Retrieved January 17, 2012.
- ^ Kelleher, James B. (2008-09-18). ""Buffett's Time Bomb Goes Off on Wall Street" by James B. Kelleher of Reuters". Reuters.com. http://www.reuters.com/article/newsOne/idUSN1837154020080918. Retrieved 2010-08-29.
- ^ Edwards, Franklin (1995), "Derivatives Can Be Hazardous To Your Health: The Case of Metallgesellschaft", Derivatives Quarterly (Spring 1995): 8–17, http://www0.gsb.columbia.edu/faculty/fedwards/papers/DerivativesCanBeHazardous.pdf
- ^ Whaley, Robert (2006). Derivatives: markets, valuation, and risk management. John Wiley and Sons. p. 506. ISBN 0-471-78632-2. http://books.google.com/books?id=Hb7xXy-wqiYC&printsec=frontcover&cad=0#v=onepage&q&f=false.
- ^ http://www.businessweek.com/news/2011-09-15/ubs-loss-shows-banks-fail-to-learn-from-kerviel-leeson.html
- ^ Story, Louise, "A Secretive Banking Elite Rules Trading in Derivatives", The New York Times, December 11, 2010 (December 12, 2010 p. A1 NY ed.). Retrieved 2010-12-12.
- Hull, John C. (2011). Options, Futures and Other Derivatives (8th ed.). Harlow: Pearson Education. ISBN 9780132604604′.
- Durbin, Michael (2011). All About Derivatives (2nd ed.). New York: McGraw-Hill. ISBN 978-0-07-174351-8.
- Mattoo, Mehraj (1997). Structured Derivatives: New Tools for Investment Management: A Handbook of Structuring, Pricing & Investor Applications. London: Financial Times. ISBN 0-273-61120-8.