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78-511: PAM was to be "a market in the future of the Middle East", and would have allowed trading of futures contracts based on possible political developments in several Middle Eastern countries. The theory behind such a market is that the monetary value of a futures contract on an event reflects the probability that that event will actually occur, since a market's actors rationally bid a contract either up or down based on reliable information. One of

156-417: A futures contract (sometimes called futures ) is a standardized legal contract to buy or sell something at a predetermined price for delivery at a specified time in the future, between parties not yet known to each other. The asset transacted is usually a commodity or financial instrument . The predetermined price of the contract is known as the forward price or delivery price . The specified time in

234-402: A buyer and seller of a futures contract or an options seller to ensure the 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

312-404: 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

390-415: A daily basis, however, in times of high volatility, a broker can make a margin call intra-day. Margin calls 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

468-455: A day, on average, for many days. This would constitute a 1% daily movement, up or down. To annualize this, you can use the "rule of 16", that is, multiply by 16 to get 16% as the annual volatility. The rationale for this is that 16 is the square root of 256, which is approximately the number of trading days in a year (252). This also uses the fact that the standard deviation of the sum of n independent variables (with equal standard deviations)

546-749: A federal betting parlor on atrocities and terrorism is ridiculous and it's grotesque", while Dorgan called it "useless, offensive and unbelievably stupid". Other critics offered similar outrage. Within less than a day, the Pentagon announced the cancellation of PAM, and by the end of the week John Poindexter , head of the DARPA unit responsible for developing it, had offered his resignation. PAM had first been proposed and funded in 2001, Poindexter joined DARPA in December 2002, and Hanson claimed that Poindexter "actually had little involvement with PAM". CNN reported

624-471: 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 . Volatility (finance) In finance , volatility (usually denoted by " σ ") is the degree of variation of a trading price series over time, usually measured by the standard deviation of logarithmic returns . Historic volatility measures

702-462: A lower volatility stock may have an expected (average) return of 7%, with annual volatility of 5%. Ignoring compounding effects, this would indicate returns from approximately negative 3% to positive 17% most of the time (19 times out of 20, or 95% via a two standard deviation rule). A higher volatility stock, with the same expected return of 7% but with annual volatility of 20%, would indicate returns from approximately negative 33% to positive 47% most of

780-402: A no-arbitrage setting when we take expectations with respect to the risk-neutral probability . In other words: a futures price is a 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. The situation where the price of a commodity for future delivery is higher than

858-411: A percentage of the value of the futures contract, must be maintained throughout the life of the contract to guarantee the agreement, as over this time the price of the contract can vary as a function of supply and demand, causing one side of the exchange to lose money at the expense of the other. To mitigate the risk of default, the product is marked to market on a daily basis where the difference between

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936-573: A predictable frequency, and the increasingly popular Heston model of stochastic volatility . [link broken] It is common knowledge that many types of assets experience periods of high and low volatility. That is, during some periods, prices go up and down quickly, while during other times they barely move at all. In foreign exchange market , price changes are seasonally heteroskedastic with periods of one day and one week. Periods when prices fall quickly (a crash ) are often followed by prices going down even more, or going up by an unusual amount. Also,

1014-444: A relationship can be summarized as: The convenience yield is not easily observable or measured, so y is often calculated, when r and u are known, as the extraneous yield paid by investors selling at spot to arbitrage the futures price. Dividend or income yields q are more easily observed or estimated, and can be incorporated in the same way: In a perfect market, the relationship between futures and spot prices depends only on

1092-420: A series of bad harvests. 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 standardized futures contracts based on commodities , as well as a number of futures exchanges set up in countries around

1170-460: 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. The expectation-based relationship will also hold in

1248-408: A swing. The job of fundamental analysts at market makers and option trading boutique firms typically entails trying to assign numeric values to these numbers. Using a simplification of the above formula it is possible to estimate annualized volatility based solely on approximate observations. Suppose you notice that a market price index, which has a current value near 10,000, has moved about 100 points

1326-406: A time series of past market prices. Implied volatility looks forward in time, being derived from the market price of a market-traded derivative (in particular, an option). Volatility as described here refers to the actual volatility , more specifically: Now turning to implied volatility , we have: For a financial instrument whose price follows a Gaussian random walk , or Wiener process ,

1404-407: A time when prices rise quickly (a possible bubble ) may often be followed by prices going up even more, or going down by an unusual amount. Most typically, extreme movements do not appear 'out of nowhere'; they are presaged by larger movements than usual or by known uncertainty in specific future events. This is termed autoregressive conditional heteroskedasticity . Whether such large movements have

1482-414: A year) is The formulas used above to convert returns or volatility measures from one time period to another assume a particular underlying model or process. These formulas are accurate extrapolations of a random walk , or Wiener process, whose steps have finite variance. However, more generally, for natural stochastic processes, the precise relationship between volatility measures for different time periods

1560-401: Is defined as the standard deviation of a sequence of random variables, each of which is the return of the fund over some corresponding sequence of (equally sized) times. Thus, "annualized" volatility σ annually is the standard deviation of an instrument's yearly logarithmic returns . The generalized volatility σ T for time horizon T in years is expressed as: Therefore, if

1638-415: Is made and the account owner must replenish the margin account. 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. To minimize counterparty risk to traders, trades executed on regulated futures exchanges are guaranteed by a clearing house . The clearing house becomes

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1716-419: 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 their margin account. Margin-equity ratio is a term used by speculators , representing

1794-636: Is more complicated. Some use the Lévy stability exponent α to extrapolate natural processes: If α  = 2 the Wiener process scaling relation is obtained, but some people believe α  < 2 for financial activities such as stocks, indexes and so on. This was discovered by Benoît Mandelbrot , who looked at cotton prices and found that they followed a Lévy alpha-stable distribution with α  = 1.7. (See New Scientist, 19 April 1997.) Much research has been devoted to modeling and forecasting

1872-627: Is not covered by low resolution volatility and vice versa. The risk parity weighted volatility of the three assets Gold, Treasury bonds and Nasdaq acting as proxy for the Marketportfolio seems to have a low point at 4% after turning upwards for the 8th time since 1974 at this reading in the summer of 2014. Some authors point out that realized volatility and implied volatility are backward and forward looking measures, and do not reflect current volatility. To address that issue an alternative, ensemble measures of volatility were suggested. One of

1950-417: Is set by the exchange. If a position involves an exchange-traded product, the amount or percentage of the 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

2028-480: Is √n times the standard deviation of the individual variables. However importantly this does not capture (or in some cases may give excessive weight to) occasional large movements in market price which occur less frequently than once a year. The average magnitude of the observations is merely an approximation of the standard deviation of the market index. Assuming that the market index daily changes are normally distributed with mean zero and standard deviation  σ ,

2106-595: 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

2184-672: The MIT Media Lab in 2003, which would permit for-profit betting on major events. There are now commercial policy-analysis markets that perform such functions. One, Intrade , had previously offered futures on events such as the capture of Osama bin Laden, the US Presidential Election, and the bombing of Iran. As of March 10, 2013, all trading had been suspended on Intrade's website due to undisclosed financial irregularities. Futures contract In finance ,

2262-497: The Tokyo Commodity Exchange (TOCOM). Today, there are more than 90 futures and futures options exchanges worldwide trading to include: Most futures contract codes are five characters. The first two characters identify the contract type, the third character identifies the month and the last two characters identify the year. On CME Group markets, third (month) futures contract codes are: Contracts expire after

2340-675: 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

2418-485: The IMM added interest rate futures on US treasury bills , and in 1982 they added stock market index futures . Although futures contracts are oriented towards a future time point, their main purpose is to mitigate the risk of default by either party in the intervening period. In this vein, the futures exchange requires both parties to put up initial cash, or a performance bond, known as the margin . Margins, sometimes set as

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2496-427: 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. When the deliverable commodity is not in plentiful supply (or when it does not yet exist) rational pricing cannot be applied, as

2574-466: The amount caused by specific events like earnings or policy announcements. For instance, a company like Microsoft would have clean volatility caused by people buying and selling on a daily basis but dirty (or event vol) events like quarterly earnings or a possibly anti-trust announcement. Breaking down volatility into two components is useful in order to accurately price how much an option is worth, especially when identifying what events may contribute to

2652-558: 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

2730-425: 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 future. In an efficient market, supply and demand would be expected to balance out at a futures price that represents the present value of an unbiased expectation of the price of the asset at the delivery date. This relationship can be represented as :: By contrast, in

2808-408: The asset to sell at the futures price. Convenience yields are benefits of holding an asset for sale at the futures price beyond the cash received from the sale. Such benefits could include the ability to meet unexpected demand, or the ability to use the asset as an input in production. Investors pay or give up the convenience yield when selling at the spot price because they give up these benefits. Such

2886-470: The band of price oscillation. In September 2019, JPMorgan Chase determined the effect of US President Donald Trump 's tweets , and called it the Volfefe index combining volatility and the covfefe meme . Volatility matters to investors for at least eight reasons, several of which are alternative statements of the same feature or are directly consequent on each other: Volatility does not measure

2964-423: 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. The initial margin

3042-418: 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

3120-423: The currency in the interval before payment is received. However, futures contracts also offer opportunities for speculation in that a trader who predicts that the price of an asset will move in a particular direction can contract to buy or sell it in the future at a price which (if the prediction is correct) will yield a profit. In particular, if the speculator is able to profit, then the underlying commodity that

3198-427: The daily logarithmic returns of a stock have a standard deviation of σ daily and the time period of returns is P in trading days, the annualized volatility is so A common assumption is that P = 252 trading days in any given year. Then, if σ daily = 0.01, the annualized volatility is The monthly volatility (i.e. T = 1 12 {\displaystyle T={\tfrac {1}{12}}} of

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3276-437: 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 futures and interest rate futures as well as for most equity (index) options, this happens on the third Friday of certain trading months. On this day the back month futures contract becomes the front-month futures contract. For example, for most CME and CBOT contracts, at

3354-452: 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

3432-402: 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. We define the forward price to be the strike K such that the contract has 0 value at

3510-430: The direction of price changes, merely their dispersion. This is because when calculating standard deviation (or variance ), all differences are squared, so that negative and positive differences are combined into one quantity. Two instruments with different volatilities may have the same expected return, but the instrument with higher volatility will have larger swings in values over a given period of time. For example,

3588-544: The expected spot price is known as contango . Markets are said to be normal when futures prices are above the current spot price and far-dated futures are priced above near-dated futures. The reverse, where the price of a commodity for future delivery is lower than the expected spot price is known as backwardation . Similarly, markets are said to be inverted when futures prices are below the current spot price and far-dated futures are priced below near-dated futures. There are many different kinds of futures contracts, reflecting

3666-602: The expected value of the magnitude of the observations is √(2/ π ) σ = 0.798 σ . The net effect is that this crude approach underestimates the true volatility by about 20%. Consider the Taylor series : Taking only the first two terms one has: Volatility thus mathematically represents a drag on the CAGR (formalized as the " volatility tax "). Realistically, most financial assets have negative skewness and leptokurtosis, so this formula tends to be over-optimistic. Some people use

3744-454: The expiration of the December contract, the March futures become the nearest contract. During a short period (perhaps 30 minutes) the underlying cash price and the futures prices 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,

3822-399: 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. Contracts on financial instruments were introduced in the 1970s by

3900-466: The formula: for a rough estimate, where k is an empirical factor (typically five to ten). Despite the sophisticated composition of most volatility forecasting models, critics claim that their predictive power is similar to that of plain-vanilla measures, such as simple past volatility especially out-of-sample, where different data are used to estimate the models and to test them. Other works have agreed, but claim critics failed to correctly implement

3978-468: The future when delivery and payment occur is known as the delivery date . Because it derives its value from the value of the underlying asset, a futures contract is a derivative . Contracts are traded at futures exchanges , which act as a marketplace between buyers and sellers. The buyer of a contract is said to be the long position holder and the selling party is said to be the short position holder. As both parties risk their counter-party reneging if

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4056-446: 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 (" rational pricing ") apply when

4134-534: The high risk trading instruments in the market. Stock market index futures are also used as indicators to determine market sentiment. The first futures contracts were negotiated for agricultural commodities, and later futures contracts were negotiated for natural resources such as oil. Financial futures were introduced in 1972, and in recent decades, currency futures , interest rate futures , stock market index futures , and cryptocurrency inverse futures and perpetual futures have played an increasingly large role in

4212-608: 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. Exchanges implement strict limits on how much exposure an entity may have closer to expiration as an effort to avoid any volatility around final settlement. When

4290-406: The initial agreed-upon price and the actual daily futures price is re-evaluated daily. This is sometimes known as the variation margin, where the futures exchange will draw money out of the losing party's margin account and put it into that of the other party, ensuring the correct loss or profit is reflected daily. If the margin account goes below a certain value set by the exchange, then a margin call

4368-407: The listing month. Therefore traders must roll over their positions into the next month code. Example: CLX14 is a Crude Oil (CL), November (X) 2014 (14) contract. Futures traders are traditionally placed in one of two groups: hedgers and speculators . Hedgers 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

4446-405: 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

4524-465: The measures is defined as the standard deviation of ensemble returns instead of time series of returns. Another considers the regular sequence of directional-changes as the proxy for the instantaneous volatility. One method of measuring Volatility, often used by quant option trading firms, divides up volatility into two components. Clean volatility - the amount of volatility caused standard events like daily transactions and general noise - and dirty vol,

4602-667: The models for PAM was a political futures market run by the University of Iowa , which had predicted US election outcomes more accurately than either opinion polls or political pundits . PAM was also inspired by the work of George Mason University economist Robin Hanson . At a July 28, 2003, press conference, US Senators Byron L. Dorgan ( D - ND ) and Ron Wyden (D- OR ) claimed that PAM would allow trading in such events as coups d'états , assassinations, and terrorist attacks, due to such events appearing on interface pictures on

4680-507: The more complicated models. Some practitioners and portfolio managers seem to completely ignore or dismiss volatility forecasting models. For example, Nassim Taleb famously titled one of his Journal of Portfolio Management papers "We Don't Quite Know What We are Talking About When We Talk About Volatility". In a similar note, Emanuel Derman expressed his disillusion with the enormous supply of empirical models unsupported by theory. He argues that, while "theories are attempts to uncover

4758-458: The overall futures markets. Even organ futures have been proposed to increase the supply of transplant organs. The original use of futures contracts mitigates the risk of price or exchange rate movements by allowing parties to fix prices or rates in advance for future transactions. This could be advantageous when (for example) a party expects to receive payment in foreign currency in the future and wishes to guard against an unfavorable movement of

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4836-694: 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

4914-418: The present time. Assuming interest rates are constant the forward price of the futures is equal to the forward price of the forward contract with the same strike and maturity. It is also the same if the underlying asset is uncorrelated with interest rates. Otherwise, the difference between the forward price on the futures (futures price) and the forward price on the asset, is proportional to the covariance between

4992-421: The price goes against them, the contract may involve both parties lodging as security a margin of the value of the contract with a mutually trusted third party. For example, in gold futures trading, the margin varies between 2% and 20% depending on the volatility of the spot market . A stock future is a cash-settled futures contract on the value of a particular stock market index . Stock futures are one of

5070-569: The program would be relaunched by the private firm, Net Exchange, that helped create it, but that the newer version "will not include any securities based on forecasts of violent events such as assassinations or terror attacks". On June 11, 2007, Popular Science launched a similar program, known as the PopSci Predictions Exchange . Another project was the American Action Market announced by Tad Hirsh of

5148-407: The project website. "On the web site, as a backdrop to bold text, were faint background sample screens. In a small (less than 2 percent) section of two such screens, Polk had included as colorful examples of possible miscellaneous items an assassination of Yasser Arafat, a missile attack by North Korea, and the overthrow of the king of Jordan." They denounced the idea, with Wyden stating, "The idea of

5226-404: The rate of risk-free return r . or, with continuous compounding This relationship may be modified for storage costs u , dividend or income yields q , and convenience yields y . Storage costs are costs involved in storing a commodity to sell at the futures price. Investors selling the asset at the spot price to arbitrage a futures price earns the storage costs they would have paid to store

5304-411: The required margin. ROM may be calculated (realized return) / (initial margin). The Annualized ROM is equal to (ROM+1) -1. For example, if a trader earns 10% on margin in two months, that would be about 77% annualized. Settlement is the act of consummating the contract, and can be done in one of two ways, as specified per type of futures contract: Expiry (or Expiration in the U.S.) is the time and

5382-473: The risk of price changes. Speculators, by contrast, 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, speculators are seeking exposure to the asset in long futures contracts or the opposite effect via short futures contracts. Hedgers typically include producers and consumers of

5460-466: The same direction, or the opposite, is more difficult to say. And an increase in volatility does not always presage a further increase—the volatility may simply go back down again. Measures of volatility depend not only on the period over which it is measured, but also on the selected time resolution, as the information flow between short-term and long-term traders is asymmetric. As a result, volatility measured with high resolution contains information that

5538-474: The speculator traded would have been saved during a time of surplus and sold during a time of need, offering the consumers of the commodity a more favorable distribution of commodity over time. The Dōjima Rice Exchange , first established in 1697 in Osaka , is considered by some to be the first futures exchange market, to meet the needs of samurai who—being paid in rice—needed a stable conversion to coin after

5616-544: The term "maintenance margin", which in effect defines 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

5694-518: The time (19 times out of 20, or 95%). These estimates assume a normal distribution ; in reality stock price movements are found to be leptokurtotic (fat-tailed). Although the Black-Scholes equation assumes predictable constant volatility, this is not observed in real markets. Amongst more realistic models are Emanuel Derman and Iraj Kani 's and Bruno Dupire 's local volatility , Poisson process where volatility jumps to new levels with

5772-461: The time will not be twice the distance from zero. Since observed price changes do not follow Gaussian distributions, others such as the Lévy distribution are often used. These can capture attributes such as " fat tails ". Volatility is a statistical measure of dispersion around the average of any random variable such as market parameters etc. For any fund that evolves randomly with time, volatility

5850-416: The underlying asset price and interest rates. For example, a futures contract on a zero-coupon bond will have a futures price lower than the forward price. This is called the futures "convexity correction". Thus, assuming constant rates, for a simple, non-dividend paying asset, the value of the futures/forward price, F(t,T) , will be found by compounding the present value S(t) at time t to maturity T by

5928-451: The volatility of financial returns, and yet few theoretical models explain how volatility comes to exist in the first place. Roll (1984) shows that volatility is affected by market microstructure . Glosten and Milgrom (1985) shows that at least one source of volatility can be explained by the liquidity provision process. When market makers infer the possibility of adverse selection , they adjust their trading ranges, which in turn increases

6006-422: The width of the distribution increases as time increases. This is because there is an increasing probability that the instrument's price will be farther away from the initial price as time increases. However, rather than increase linearly, the volatility increases with the square-root of time as time increases, because some fluctuations are expected to cancel each other out, so the most likely deviation after twice

6084-633: The world. By 1875 cotton futures were being traded in Bombay in India and within a few years this had expanded to futures on edible oilseeds complex , raw jute and jute goods and bullion . In the 1930s two thirds of all futures was in wheat. The 1972 creation of the International Monetary Market (IMM) by the Chicago Mercantile Exchange was the world's first financial futures exchange, and launched currency futures . In 1976,

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