661:, depending on the option. The market price of an American-style option normally closely follows that of the underlying stock being the difference between the market price of the stock and the strike price of the option. The actual market price of the option may vary depending on a number of factors, such as a significant option holder needing to sell the option due to the expiration date approaching and not having the financial resources to exercise the option, or a buyer in the market trying to amass a large option holding. The ownership of an option does not generally entitle the holder to any rights associated with the underlying asset, such as voting rights or any income from the underlying asset, such as a
1021:
921:
975:
1244:, in which a trader buys a stock (or holds a previously-purchased long stock position), and buys a put. This strategy acts as an insurance when investing long on the underlying stock, hedging the investor's potential losses, but also shrinking an otherwise larger profit, if just purchasing the stock without the put. The maximum profit of a protective put is theoretically unlimited as the strategy involves being long on the underlying stock. The maximum loss is limited to the purchase price of the underlying stock less the strike price of the put option and the premium paid. A protective put is also known as a married put.
56:
1065:
situation, the trader can realise an immediate profit. Alternatively, the trader can exercise the option – for example, if there is no secondary market for the options – and then sell the stock, realising a profit. A trader would make a profit if the spot price of the shares rises by more than the premium. For example, if the exercise price is 100 and the premium paid is 10, then if the spot price of 100 rises to only 110, the transaction is break-even; an increase in the stock price above 110 produces a profit.
646:
the underlying asset, while a put option would normally be exercised only when the strike price is above the market value. When an option is exercised, the cost to the option holder is the strike price of the asset acquired plus the premium, if any, paid to the issuer. If the option's expiration date passes without the option being exercised, the option expires, and the holder forfeits the premium paid to the issuer. In any case, the premium is income to the issuer, and normally a capital loss to the option holder.
2914:
specific options strategies permitted at each level, vary between brokers. Brokers may also have their own specific vetting criteria, but they are usually based on factors such as the trader's annual salary and net worth, trading experience, and investment goals (capital preservation, income, growth, or speculation). For example, a trader with a low salary and net worth, little trading experience, and only concerned about preserving capital generally would not be permitted to execute high-risk strategies like
857:
1161:
1153:
1105:
1126:
1046:
1077:
5015:
1169:
1089:
stock price at expiration is above the exercise price, the trader lets the put contract expire and loses only the premium paid. In the transaction, the premium also plays a role as it enhances the break-even point. For example, if the exercise price is 100 and the premium paid is 10, then a spot price between 90 and 100 is not profitable. The trader makes a profit only if the spot price is below 90.
2056:. A trinomial tree option pricing model can be shown to be a simplified application of the explicit finite difference method. Although the finite difference approach is mathematically sophisticated, it is particularly useful where changes are assumed over time in model inputs – for example dividend yield, risk-free rate, or volatility, or some combination of these – that are not
1225:.) If the stock price rises above the exercise price, the call will be exercised and the trader will get a fixed profit. If the stock price falls, the call will not be exercised, and any loss incurred to the trader will be partially offset by the premium received from selling the call. Overall, the payoffs match the payoffs from selling a put. This relationship is known as
2982:(ISE) is an electronic options exchange located in New York City. Launched in 2000, ISE was the first all-electronic U.S. options exchange. ISE provides options trading on U.S. equities, indexes, and ETFs. Its trading platform provides a maximum price improvement auction to allow market makers to compete for orders. ISE is regulated by the SEC and is owned by Nasdaq, Inc.
717:. Privileges were options sold over the counter in nineteenth-century America, with both puts and calls on shares offered by specialized dealers. Their exercise price was fixed at a rounded-off market price on the day or week that the option was bought, and the expiry date was generally three months after purchase. They were not traded in secondary markets.
634:(market price) of the underlying security or commodity on the day an option is issued, or it may be fixed at a discount or at a premium. The issuer has the corresponding obligation to fulfill the transaction (to sell or buy) if the holder "exercises" the option. An option that conveys to the holder the right to buy at a specified price is referred to as a
1134:(put writer) makes a profit in the amount of the premium. If the stock price at expiration is below the strike price by more than the amount of the premium, the trader loses money, with the potential loss being up to the strike price minus the premium. A benchmark index for the performance of a cash-secured short put option position is the
1061:) at a later date, rather than purchase the stock outright. The cash outlay on the option is the premium. The trader would have no obligation to buy the stock, but only has the right to do so on or before the expiration date. The risk of loss would be limited to the premium paid, unlike the possible loss had the stock been bought outright.
2938:(CBOE) is an options exchange located in Chicago, Illinois. Founded in 1973, the CBOE is the first options exchange in the United States. The CBOE offers options trading on various underlying securities including market indexes, exchange-traded funds (ETFs), stocks, and volatility indexes. Its flagship product is options on the
1974:
value can approximate the theoretical value produced by Black–Scholes, to the desired degree of precision. However, the binomial model is considered more accurate than Black–Scholes because it is more flexible; e.g., discrete future dividend payments can be modeled correctly at the proper forward time steps, and
2901:. In an option contract this risk is that the seller will not sell or buy the underlying asset as agreed. The risk can be minimized by using a financially strong intermediary able to make good on the trade, but in a major panic or crash the number of defaults can overwhelm even the strongest intermediaries.
1973:
intervals over the option's life. The model starts with a binomial tree of discrete future possible underlying stock prices. By constructing a riskless portfolio of an option and stock (as in the Black–Scholes model) a simple formula can be used to find the option price at each node in the tree. This
690:
harvest would be larger than usual, and during the off-season, he acquired the right to use a number of olive presses the following spring. When spring came and the olive harvest was larger than expected, he exercised his options and then rented the presses out at a much higher price than he paid for
2913:
systems to restrict traders from executing certain options strategies that would not be suitable for them. Brokers generally offer about four or five approval levels, with the lowest level offering the lowest risk and the highest level offering the highest risk. The actual numbers of levels, and the
1088:
to sell the stock at a fixed price (strike price) at a later date. The trader is not obligated to sell the stock, but has the right to do so on or before the expiration date. If the stock price at expiration is below the exercise price by more than the premium paid, the trader makes a profit. If the
724:
market, call options have long been used to assemble large parcels of land from separate owners; e.g., a developer pays for the right to buy several adjacent plots, but is not obligated to buy these plots and might not unless they can buy all the plots in the entire parcel. Additionally, purchase of
2966:
is an options and futures exchange located in
Philadelphia, Pennsylvania. It is the oldest stock exchange in the United States. The NASDAQ OMX PHLX allows trading of options on equities, indexes, ETFs, and foreign currencies. It is one of the few exchanges designated for trading currency options in
645:
The issuer may grant an option to a buyer as part of another transaction (such as a share issue or as part of an employee incentive scheme), or the buyer may pay a premium to the issuer for the option. A call option would normally be exercised only when the strike price is below the market value of
1982:
is a similar model, allowing for an up, down or stable path; although considered more accurate, particularly when fewer time-steps are modelled, it is less commonly used as its implementation is more complex. For a more general discussion, as well as for application to commodities, interest rates
1133:
A trader who expects a stock's price to increase can buy the stock or instead sell, or "write", a put. The trader selling a put has an obligation to buy the stock from the put buyer at a fixed price ("strike price"). If the stock price at expiration is above the strike price, the seller of the put
1116:
or instead sell, or "write", a call. The trader selling a call has an obligation to sell the stock to the call buyer at a fixed price ("strike price"). If the seller does not own the stock when the option is exercised, they are obligated to purchase the stock in the market at the prevailing market
2993:
is a derivatives exchange located in
Frankfurt, Germany. It offers trading in futures and options on interest rates, equities, indexes, and fixed-income products. Formed in 1998 from the merger of Deutsche Terminbörse (DTB) and Swiss Options and Financial Futures Exchange (SOFFEX), Eurex Exchange
936:
options (OTC options, also called "dealer options") are traded between two private parties and are not listed on an exchange. The terms of an OTC option are unrestricted and may be individually tailored to meet any business need. In general, the option writer is a well-capitalized institution (to
1064:
The holder of an
American-style call option can sell the option holding at any time until the expiration date and would consider doing so when the stock's spot price is above the exercise price, especially if the holder expects the price of the option to drop. By selling the option early in that
629:
An option is a contract that allows the holder the right to buy or sell an underlying asset or financial instrument at a specified strike price on or before a specified date, depending on the form of the option. Selling or exercising an option before expiry typically requires a buyer to pick the
2888:
can arise when the underlying closes at or very close to the option's strike value on the last day the option is traded prior to expiration. The option writer (seller) may not know with certainty whether or not the option will actually be exercised or be allowed to expire. Therefore, the option
1639:
in
Economics), the application of the model in actual options trading is clumsy because of the assumptions of continuous trading, constant volatility, and a constant interest rate. Nevertheless, the Black–Scholes model is still one of the most important methods and foundations for the existing
1619:
made a major breakthrough by deriving a differential equation that must be satisfied by the price of any derivative dependent on a non-dividend-paying stock. By employing the technique of constructing a risk-neutral portfolio that replicates the returns of holding an option, Black and
Scholes
2866:
959:
By avoiding an exchange, users of OTC options can narrowly tailor the terms of the option contract to suit individual business requirements. In addition, OTC option transactions generally do not need to be advertised to the market and face little or no regulatory requirements. However, OTC
2097:
A call option (also known as a CO) expiring in 99 days on 100 shares of XYZ stock is struck at $ 50, with XYZ currently trading at $ 48. With future realized volatility over the life of the option estimated at 25%, the theoretical value of the option is $ 1.89. The hedge parameters
2005:
because of the complexity of the instrument. In these cases, a Monte Carlo approach may often be useful. Rather than attempt to solve the differential equations of motion that describe the option's value in relation to the underlying security's price, a Monte Carlo model uses
2314:
Under this scenario, the value of the option increases by $ 0.0614 to $ 1.9514, realizing a profit of $ 6.14. Note that for a delta neutral portfolio, whereby the trader had also sold 44 shares of XYZ stock as a hedge, the net loss under the same scenario would be ($ 15.86).
1117:
price. If the stock price decreases, the seller of the call (call writer) makes a profit in the amount of the premium. If the stock price increases over the strike price by more than the amount of the premium, the seller loses money, with the potential loss being unlimited.
3006:(TSE) is a stock exchange located in Tokyo, Japan. In addition to equities, the TSE also provides trading in stock index futures and options. Trading is conducted electronically as well as through auction bidding by securities companies. The TSE is regulated by the
2307:
2178:
are (0.439, 0.0631, 9.6, and −0.022), respectively. Assume that on the following day, XYZ stock rises to $ 48.5 and volatility falls to 23.5%. We can calculate the estimated value of the call option by applying the hedge parameters to the new model inputs as:
1441:
Because the values of option contracts depend on a number of different variables in addition to the value of the underlying asset, they are complex to value. There are many pricing models in use, although all essentially incorporate the concepts of
2664:, provided the changes in these values are small. This technique can be used effectively to understand and manage the risks associated with standard options. For instance, by offsetting a holding in an option with the quantity
2429:
1187:
spread (long one X1 call, short two X2 calls, and long one X3 call) allows a trader to profit if the stock price on the expiration date is near the middle exercise price, X2, and does not expose the trader to a large loss.
2719:
1668:
for options of lower strike prices is typically higher than for higher strike prices, suggesting that volatility varies both for time and for the price level of the underlying security – a so-called
784:
options are written as bilateral, customized contracts between a single buyer and seller, one or both of which may be a dealer or market-maker. Options are part of a larger class of financial instruments known as
3186:. 1688. Portions Descriptive of the Amsterdam Stock Exchange Selected and Translated by Professor Hermann Kellenbenz. Baker Library, Harvard Graduate School Of Business Administration, Boston, Massachusetts.
2889:
writer may end up with a large, unwanted residual position in the underlying when the markets open on the next trading day after expiration, regardless of his or her best efforts to avoid such a residual.
1195:
is a strategy similar to a butterfly spread, but with different strikes for the short options – offering a larger likelihood of profit but with a lower net credit compared to the butterfly spread.
1203:(selling both a put and a call at the same exercise price) would give a trader a greater profit than a butterfly if the final stock price is near the exercise price, but might result in a large loss.
1632:
1068:
If the stock price at expiration is lower than the exercise price, the holder of the option at that time will let the call contract expire and lose only the premium (or the price paid on transfer).
2326:
from holding an option varies non-linearly with the value of the underlying and other factors. Therefore, the risks associated with holding options are more complicated to understand and predict.
1586:
More advanced models can require additional factors, such as an estimate of how volatility changes over time and for various underlying price levels, or the dynamics of stochastic interest rates.
773:
was established in 1973, which set up a regime using standardized forms and terms and trade through a guaranteed clearing house. Trading activity and academic interest have increased since then.
2187:
1871:, this can be a big simplification; regardless, the framework is often preferred for models of higher dimension. Note that for the simpler options here, i.e. those mentioned initially, the
1176:
Combining any of the four basic kinds of option trades (possibly with different exercise prices and maturities) and the two basic kinds of stock trades (long and short) allows a variety of
4095:
Bloss, Michael; Ernst, Dietmar; Häcker
Joachim (2008): Derivatives – An authoritative guide to derivatives for financial intermediaries and investors Oldenbourg Verlag München
2595:
Thus, at any point in time, one can estimate the risk inherent in holding an option by calculating its hedge parameters and then estimating the expected change in the model inputs,
3839:
2685:
2639:
2567:
2517:
2497:
2477:
2457:
2176:
2156:
2136:
2116:
1210:
which is also constructed by a call and a put, but whose strikes are different, reducing the net debit of the trade, but also reducing the risk of loss in the trade.
2010:
to generate random price paths of the underlying asset, each of which results in a payoff for the option. The average of these payoffs can be discounted to yield an
604:
Options are typically acquired by purchase, as a form of compensation, or as part of a complex financial transaction. Thus, they are also a form of asset and have a
1750:
3648:
2709:
847:
the terms by which the option is quoted in the market to convert the quoted price into the actual premium – the total amount paid by the holder to the writer
2662:
2616:
2590:
2544:
1770:
1396:
option – any option with the general characteristic that the underlying security's price must pass a certain level or "barrier" before it can be exercised.
4852:
1469:) of the underlying price with a mathematical method which returns the premium as a function of the assumed behavior. The models range from the (prototypical)
1404:
option – An all-or-nothing option that pays the full amount if the underlying security meets the defined condition on expiration, otherwise, it expires.
4106:
4764:
1704:. One principal advantage of the Heston model, however, is that it can be solved in closed form, while other stochastic volatility models require complex
2346:
1318:, which a company awards to their employees as a form of incentive compensation. Other types of options exist in many financial contracts. For example
1554:. These models are implemented using a variety of numerical techniques. In general, standard option valuation models depend on the following factors:
2861:{\displaystyle d\Pi =\Delta dS+\Gamma {\frac {dS^{2}}{2}}+\kappa d\sigma +\theta dt-\Delta dS=\Gamma {\frac {dS^{2}}{2}}+\kappa d\sigma +\theta dt\,}
1788:
noted that there is a unique diffusion process consistent with the risk neutral densities derived from the market prices of
European options. See
2942:
Index (SPX), one of the most actively traded options globally. In addition to its floor-based open outcry trading, the CBOE also operates an all-
4058:
2691:
portfolio that is hedged from loss for small changes in the underlying's price. The corresponding price sensitivity formula for this portfolio
2322:
As with all securities, trading options entails the risk of the option's value changing over time. However, unlike traditional securities, the
1864:
999:
and execute transactions. As an intermediary to both sides of the transaction, the benefits the exchange provides to the transaction include:
2044:
can be derived, and the valuation obtained. A number of implementations of finite difference methods exist for option valuation, including:
1264:
Put options give the holder the right – but not the obligation – to sell something at a specific price for a specific time period.
1261:
Call options give the holder the right – but not the obligation – to buy something at a specific price for a specific time period.
4558:
4133:
2027:
4074:
Reilly, Frank and Keith C. Brown, Investment
Analysis and Portfolio Management, 7th edition, Thompson Southwestern, 2003, pp. 994–5.
1785:
553:
4563:
1033:
These trades are described from the point of view of a speculator. If they are combined with other positions, they can also be used in
3685:
1867:. And some of the short rate models can be straightforwardly expressed in the HJM framework.) For some purposes, e.g., valuation of
1217:, in which a trader buys a stock (or holds a previously purchased stock position), and sells a call. (This can be contrasted with a
3164:
Mattias Sander. Bondesson's
Representation of the Variance Gamma Model and Monte Carlo Option Pricing. Lunds Tekniska Högskola 2008
4898:
3816:
2947:
683:
4588:
3356:
1996:
1183:
Strategies are often used to engineer a particular risk profile to movements in the underlying security. For example, buying a
4100:
4042:
4016:
3982:
Hill, Joanne, Venkatesh
Balasubramanian, Krag (Buzz) Gregory, and Ingrid Tierens. "Finding Alpha via Covered Index Writing".
3949:
Feldman, Barry and Dhuv Roy. "Passive Options-Based Investment Strategies: The Case of the CBOE S&P 500 BuyWrite Index".
3753:
3632:
3581:
1849:
1807:
1697:
1474:
844:, for instance, whether the writer must deliver the actual asset on exercise, or may simply tender the equivalent cash amount
420:
3328:
1428:
1627:
While the ideas behind the Black–Scholes model were ground-breaking and eventually led to Scholes and Merton receiving the
960:
counterparties must establish credit lines with each other and conform to each other's clearing and settlement procedures.
886:(OCC). Since the contracts are standardized, accurate pricing models are often available. Exchange-traded options include:
2302:{\displaystyle dC=(0.439\cdot 0.5)+\left(0.0631\cdot {\frac {0.5^{2}}{2}}\right)+(9.6\cdot -0.015)+(-0.022\cdot 1)=0.0614}
4720:
1860:
1565:
of the option, particularly in relation to the current market price of the underlying (in the money vs. out of the money)
1538:
As above, the value of the option is estimated using a variety of quantitative techniques, all based on the principle of
3659:
706:), explaining that "there will be only limited risks to you, while the gain may surpass all your imaginings and hopes."
4077:
Schneeweis, Thomas, and Richard Spurgin. "The Benefits of Index Option-Based Strategies for Institutional Portfolios"
4456:
4003:
3970:
3797:
3605:
3455:
3282:
3255:
3205:
3140:
3059:
2979:
2971:
acquired the Philadelphia Stock Exchange and renamed it NASDAQ OMX PHLX. It operates as a subsidiary of NASDAQ, Inc.
1516:, which depends on a set of other factors which, through a multi-variable, non-linear interrelationship, reflect the
801:. Option contracts may be quite complicated; however, at minimum, they usually contain the following specifications:
746:
give the potential borrower the right – but not the obligation – to borrow within a specified time period.
1092:
The trader exercising a put option on a stock does not need to own the underlying asset, because most stocks can be
757:
into common stock at the buyer's option, or may be called (bought back) at specified prices at the issuer's option.
709:
In London, puts and "refusals" (calls) first became well-known trading instruments in the 1690s during the reign of
695:
4958:
4126:
4008:
1848:
by describing the future evolution of the short rate. The other major framework for interest rate modelling is the
875:
621:(OTC) transactions, or they may be exchange-traded in live, public markets in the form of standardized contracts.
3228:
1918:
1889:
Once a valuation model has been chosen, there are a number of different techniques used to implement the models.
1620:
produced a closed-form solution for a European option's theoretical price. At the same time, the model generates
995:. By publishing continuous, live markets for option prices, an exchange enables independent parties to engage in
546:
1388:
option – an option whose payoff is determined by the average underlying price over some preset time period.
4893:
4538:
4067:
3749:
3245:
3039:
2935:
1966:
1942:
1837:
1234:
1135:
770:
395:
17:
3812:
1180:. Simple strategies usually combine only a few trades, while more complicated strategies can combine several.
4065:
Moran, Matthew. "Risk-adjusted Performance for Derivatives-based Indexes – Tools to Help Stabilize Returns".
2087:
2033:
1978:
can be modeled as well as European ones. Binomial models are widely used by professional option traders. The
522:
344:
1436:
1432:
1020:
3495:
3417:
3084:
920:
908:
883:
827:, also known as the exercise price, which is the price at which the underlying transaction will occur upon
4933:
4471:
4325:
4119:
3069:
3029:
2963:
2943:
2922:. Traders can update their information when requesting permission to upgrade to a higher approval level.
1825:
974:
914:
777:
761:
borrowers have long had the option to repay the loan early, which corresponds to a callable bond option.
658:
70:
3472:
797:
A financial option is a contract between two counterparties with the terms of the option specified in a
678:
Contracts similar to options have been used since ancient times. The first reputed option buyer was the
5040:
4789:
4730:
4552:
3397:
2037:
1868:
933:
781:
776:
Today, many options are created in a standardized form and traded through clearing houses on regulated
733:, which offers the buyer the right to buy the property at the set terms, including the purchase price.
654:
617:
539:
296:
2994:
operates electronic and open outcry trading platforms. Eurex Exchange is owned by Eurex Frankfurt AG.
4834:
4645:
3007:
2053:
1833:
1589:
The following are some principal valuation techniques used in practice to evaluate option contracts.
1003:
Fulfillment of the contract is backed by the credit of the exchange, which typically has the highest
902:
405:
1330:. However, many of the valuation and risk management principles apply across all financial options.
4953:
4948:
3994:
3741:
3576:(6th ed.), London: Prentice-Hall, Chapter 1 'Financial WMDs – derivatives demagoguery,' p.22,
2898:
2041:
1958:
897:
879:
4903:
4603:
4573:
4548:
4431:
4272:
4204:
3024:
2520:
2081:
1984:
1970:
1948:
1930:
1926:
1906:
1773:
1598:
1547:
1470:
608:
that may depend on a complex relationship between underlying asset price, time until expiration,
225:
2592:
are unit changes in the underlying's price, the underlying's volatility and time, respectively.
1693:
4700:
4685:
4650:
4593:
2007:
1902:
1789:
1412:
option – any of a broad category of options that may include complex financial structures.
968:
710:
370:
3721:
2667:
2621:
2549:
1380:
option – an option that may be exercised only on specified dates on or before expiration.
740:
giving the right – but not the obligation – to dramatize a specific book or script.
5045:
4913:
4680:
4578:
4257:
3104:
2502:
2482:
2462:
2442:
2161:
2141:
2121:
2101:
2069:
1701:
1685:
1649:
1315:
1037:. An option contract in US markets usually represents 100 shares of the underlying security.
987:
The most common way to trade options is via standardized options contracts listed by various
502:
415:
31:
4867:
4824:
4814:
4804:
4799:
4525:
4466:
4401:
4355:
4350:
4224:
4184:
4151:
3493:
Black, Fischer; Scholes, Myron (1973). "The Pricing of Options and Corporate Liabilities".
3011:
3003:
1884:
1841:
1728:
1716:
1628:
1579:
1572:
1568:
The cost of holding a position in the underlying security, including interest and dividends
1533:
1443:
1422:
1356:
841:
834:
605:
594:
586:
349:
252:
3696:
2694:
8:
4872:
4660:
4583:
4406:
3737:
3552:
Black, Fischer and Myron S. Scholes. "The Pricing of Options and Corporate Liabilities",
3410:
2323:
1954:
1661:
1543:
1459:
1226:
1184:
786:
737:
527:
3940:
Fischer Black and Myron S. Scholes. "The Pricing of Options and Corporate Liabilities",
2644:
2598:
2572:
2526:
4923:
4908:
4877:
4862:
4829:
4695:
4486:
4451:
4214:
4179:
4142:
4052:
3998:
3963:
Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets
3570:
3520:
3512:
3220:
3114:
3079:
2885:
1898:
1755:
1674:
1665:
1497:
In its most basic terms, the value of an option is commonly decomposed into two parts:
1466:
1352:
1323:
1274:
Physical delivery option requires actual delivery of the goods or stocks to take place.
1207:
1177:
828:
714:
517:
475:
460:
430:
354:
282:
199:
77:
65:
630:
contract up at the agreed upon price. The strike price may be set by reference to the
4928:
4918:
4857:
4844:
4819:
4705:
4491:
4287:
4096:
4038:
4022:
4012:
3966:
3793:
3628:
3601:
3577:
3524:
3451:
3393:
3251:
3201:
3044:
2519:
are the standard hedge parameters calculated from an option valuation model, such as
2057:
2011:
2002:
1705:
1455:
1229:
and offers insights for financial theory. A benchmark index for the performance of a
609:
450:
445:
435:
380:
206:
174:
2335:
4809:
4748:
4743:
4725:
4655:
4421:
4416:
4388:
4340:
4219:
3572:
Traders, Guns & Money: Knowns and unknowns in the dazzling world of derivatives
3504:
3094:
2437:
2424:{\displaystyle dC=\Delta dS+\Gamma {\frac {dS^{2}}{2}}+\kappa d\sigma +\theta dt\,}
1914:
1829:
1801:
1712:
1670:
1655:
1621:
1608:
1551:
1192:
1147:
988:
964:
754:
650:
497:
492:
465:
335:
306:
247:
211:
159:
47:
5019:
4989:
4984:
4938:
4774:
4769:
4715:
4625:
4533:
4506:
4446:
4441:
4411:
4360:
4345:
4262:
4242:
3990:
3768:
3745:
3334:
3074:
3034:
2959:
2049:
2045:
2015:
1975:
1962:
1922:
1604:
1113:
1093:
1034:
996:
730:
455:
440:
400:
216:
154:
115:
110:
2014:
for the option. Note though, that despite its flexibility, using simulation for
878:. Exchange-traded options have standardized contracts and are settled through a
55:
4994:
4979:
4779:
4690:
4640:
4617:
4598:
4426:
4368:
4335:
4330:
4310:
4234:
3958:
3860:
3089:
3054:
2990:
2910:
1979:
1845:
1821:
1781:
1520:
1392:
1241:
971:. These must either be exercised by the original grantee or allowed to expire.
948:
750:
743:
679:
470:
375:
325:
287:
179:
126:
120:
100:
95:
3975:
3874:
2068:
Other numerical implementations which have been used to value options include
1344:
Options are classified into a number of styles, the most common of which are:
638:, while one that conveys the right to sell at a specified price is known as a
578:, the right, but not the obligation, to buy or sell a specific quantity of an
5034:
4974:
4943:
4784:
4710:
4670:
4665:
4501:
4373:
4320:
4315:
4297:
4194:
4174:
4026:
3224:
3109:
3099:
2688:
1721:
1616:
1612:
1486:
1408:
1400:
1327:
992:
937:
prevent credit risk). Option types commonly traded over the counter include:
856:
758:
410:
385:
237:
184:
3950:
3888:
4794:
4568:
4496:
4476:
4436:
4305:
4277:
4267:
4209:
3726:
1777:
1689:
1562:
1539:
1478:
1447:
1384:
1339:
1319:
1214:
1058:
824:
598:
590:
512:
487:
257:
149:
144:
135:
105:
1852:(HJM). The distinction is that HJM gives an analytical description of the
1016:
Maintenance of orderly markets, especially during fast trading conditions.
4675:
4543:
4514:
4510:
4461:
4252:
4247:
4035:
Option Volatility and Pricing: Advanced Trading Strategies and Techniques
3764:
1910:
1872:
1856:
1813:
1636:
1054:
1013:
Enforcement of market regulation to ensure fairness and transparency, and
1004:
893:
806:
721:
635:
507:
320:
277:
272:
262:
169:
86:
4107:"Why We Have Never Used the Black–Scholes–Merton Option Pricing Formula"
3942:
3553:
1160:
1152:
4999:
4635:
4630:
4396:
4282:
3516:
3447:
2939:
2915:
1925:, closed form solutions are not available; approximations here include
1859:, rather than just the short rate. (The HJM framework incorporates the
1681:
1517:
1506:
1482:
1218:
1085:
817:
810:
798:
749:
Many choices, or embedded options, have traditionally been included in
725:
real property, like houses, requires a buyer paying the seller into an
639:
631:
612:, the risk-free rate of interest, and the strike price of the option.
579:
27:
Right to buy or sell a certain thing at a later date at an agreed price
3198:
History of the Global Stock Market from Ancient Rome to Silicon Valley
874:
Exchange-traded options (also called "listed options") are a class of
4189:
4111:
4086:
Whaley, Robert. "Risk and Return of the CBOE BuyWrite Monthly Index"
3064:
2919:
2334:
In general, the change in the value of an option can be derived from
1776:, where the volatility is a constant. The concept was developed when
1640:
financial market in which the result is within the reasonable range.
1505:, which is defined as the difference between the market value of the
1451:
1230:
1222:
3840:"50 Years of Exchange-Traded Options. Cboe Marks Golden Anniversary"
3787:
3261:
1112:
A trader who expects a stock's price to decrease can sell the stock
1104:
4759:
4481:
4378:
4199:
3508:
2879:
1817:
1200:
1125:
1045:
952:
837:
date, or expiry, which is the last date the option can be exercised
703:
662:
232:
2001:
For many classes of options, traditional valuation techniques are
1921:
applies to an American call with one dividend, for other cases of
1314:
Another important class of options, particularly in the U.S., are
1076:
4088:
4079:
3983:
3913:
2897:
A further, often ignored, risk in derivatives such as options is
567:
482:
425:
1772:. As such, a local volatility model is a generalisation of the
5014:
2968:
1969:. It models the dynamics of the option's theoretical value for
1913:. The resulting solutions are readily computable, as are their
1168:
726:
30:"Stock option" redirects here. For the employee incentive, see
3305:
2032:
The equations used to model the option are often expressed as
1582:
of the underlying security's price over the life of the option
649:
An option holder may on-sell the option to a third party in a
3965:, 4th edition, World Scientific (Singapore, 2004); Paperback
3247:
Options, Futures and Other Derivatives (excerpt by Fan Zhang)
3049:
1429:
Mathematical finance § Derivatives pricing: the Q world
1365:
option – an option that may only be exercised on expiry.
687:
582:
164:
1624:
necessary for effective risk management of option holdings.
686:. On a certain occasion, it was predicted that the season's
3421:
1084:
A trader who expects a stock's price to decrease can buy a
1053:
A trader who expects a stock's price to increase can buy a
390:
2974:
991:. Listings and prices are tracked and can be looked up by
3119:
1575:
together with any restrictions on when exercise may occur
1277:
Cash-settled option is settled in resulting cash payment.
2930:
2018:
is somewhat more complex than for lattice based models.
1696:
for a discussion of the logic. Other models include the
924:
Average Option Volume (90 days) vs Market Capitalization
4105:
Espen Gaarder Haug & Nassim Nicholas Taleb (2008):
1953:
Closely following the derivation of Black and Scholes,
1465:
The valuation itself combines a model of the behavior (
1024:
Days till Expiration vs Option Volume (7000+ contracts)
1322:
are often used to assemble large parcels of land, and
2722:
2697:
2670:
2647:
2624:
2601:
2575:
2552:
2529:
2505:
2485:
2465:
2445:
2349:
2190:
2164:
2144:
2124:
2104:
1758:
1731:
1711:
An alternate, though related, approach is to apply a
1281:
978:
Option Volume vs Open Interest (for 7000+ Contracts)
3683:
3333:, International Securities Exchange, archived from
1875:can instead be employed, with certain assumptions.
1828:(effectively options on the interest rate) various
1558:
The current market price of the underlying security
769:Options contracts have been known for decades. The
3569:
2860:
2703:
2679:
2656:
2633:
2610:
2584:
2561:
2538:
2511:
2491:
2471:
2451:
2423:
2301:
2170:
2150:
2130:
2110:
1764:
1744:
1550:. More sophisticated models are used to model the
860:Put Volume vs. Call Volume (90-Day Average Volume)
805:whether the option holder has the right to buy (a
3542:(7th ed.). Thomson Southwestern. Chapter 23.
3284:Characteristics and Risks of Standardized Options
2687:of shares in the underlying, a trader can form a
1680:The main approach here is to treat volatility as
1268:
1255:
615:Options may be traded between private parties in
5032:
3875:"Nasdaq International Securities Exchange (ISE)"
3748:. 1979. Options pricing: a simplified approach,
1844:. These models describe the future evolution of
1028:
738:film or theatrical producers often buy an option
3813:"Investor Bulletin: Opening an Options Account"
3789:Basic Black–Scholes: Option Pricing and Trading
1643:
1546:in their solution. The most basic model is the
1433:Financial modeling § Quantitative finance
3625:The Volatility Surface, A Practitioner's Guide
3358:Google unveils unorthodox stock option auction
1936:
1437:Financial economics § Derivative pricing
820:asset(s) (e.g., 100 shares of XYZ Co. B stock)
574:is a contract which conveys to its owner, the
4127:
3763:
3141:"History of Financial Options - Investopedia"
2997:
1832:have been developed (applicable, in fact, to
673:
624:
547:
3646:
3622:
3540:Investment Analysis and Portfolio Management
3492:
3354:
3219:
2329:
2028:Finite difference methods for option pricing
3618:
3616:
3537:
3200:, University of Chicago Press, p. 20,
2021:
928:
4134:
4120:
4057:: CS1 maint: location missing publisher (
3538:Reilly, Frank K.; Brown, Keith C. (2003).
3250:(6th ed.), Prentice-Hall, p. 6,
2904:
1509:, and the strike price of the given option
1489:for a listing of the various models here.
869:
792:
554:
540:
4032:
2857:
2420:
1725:function of both the current asset level
1252:Options can be classified in a few ways.
4071:. (Fourth Quarter, 2002) pp. 34–40.
3613:
2088:Financial risk management § Banking
1836:generally). The best known of these are
1167:
1159:
1151:
1124:
1103:
1075:
1057:to purchase the stock at a fixed price (
1044:
1019:
973:
919:
855:
4959:Power reverse dual-currency note (PRDC)
4899:Constant proportion portfolio insurance
3989:
3817:U.S. Securities and Exchange Commission
3441:
3233:(7th ed.), McGraw-Hill, Chapter 20
3138:
2975:International Securities Exchange (ISE)
2948:U.S. Securities and Exchange Commission
1878:
764:
753:contracts. For example, many bonds are
702:" on the Amsterdam stock exchange (now
14:
5033:
4141:
4080:The Journal of Alternative Investments
3693:Quantitative Strategies Research Notes
3684:Derman, E.; Iraj Kani (January 1994).
3677:
3640:
3598:Options, Futures and Other Derivatives
3378:
1997:Monte Carlo methods for option pricing
1965:developed the original version of the
1901:and using analytical methods, develop
1892:
1492:
1481:where volatility itself is considered
1156:Payoffs from buying a butterfly spread
4115:
3837:
3785:
3444:The Handbook of Financial Instruments
3195:
3189:
2931:Chicago Board Options Exchange (CBOE)
1990:
1309:
1141:
4894:Collateralized debt obligation (CDO)
3986:. (Sept.-Oct. 2006). pp. 29–46.
3595:
3470:
3450:: John Wiley and Sons. p. 471.
3243:
2925:
2892:
1795:
1351:option – an option that may be
1240:Another very common strategy is the
3567:
3400:for typical size of option contract
3383:, Oxford University Press, pp.26–27
1664:, it has been observed that market
1527:
982:
882:with fulfillment guaranteed by the
864:
24:
3934:
3792:, Timothy Crack, pp. 91–102,
3355:Elinor Mills (December 12, 2006),
3275:
2953:
2936:The Chicago Board Options Exchange
2808:
2796:
2744:
2732:
2726:
2698:
2674:
2466:
2446:
2371:
2359:
2125:
2105:
2040:). Once expressed in this form, a
1633:Prize for Achievement in Economics
1282:According to the underlying assets
963:With few exceptions, there are no
25:
5057:
4004:Concise Encyclopedia of Economics
3139:Abraham, Stephan (May 13, 2010).
3060:International Securities Exchange
2985:
2980:International Securities Exchange
2082:Derivative (finance) § Risks
1523:of that difference at expiration.
851:
5013:
4092:, (Winter 2002), pp. 35–42.
4083:, (Spring 2001), pp. 44–52.
4009:Library of Economics and Liberty
3418:The Options Clearing Corporation
1897:In some cases, one can take the
1592:
1355:on any trading day on or before
1333:
1326:options are usually included in
1010:Counterparties remain anonymous,
944:Currency cross rate options, and
736:In the motion picture industry,
54:
3906:
3881:
3867:
3853:
3831:
3805:
3779:
3757:
3731:
3714:
3695:. Goldman Sachs. Archived from
3600:(6th ed.), Prentice-Hall,
3589:
3561:
3546:
3531:
3486:
3464:
3435:
3403:
3387:
3372:
3348:
3321:
3230:Principles of Corporate Finance
2946:. The CBOE is regulated by the
2063:
1673:; and with a time dimension, a
1373:options. Other styles include:
1235:CBOE S&P 500 BuyWrite Index
1213:One well-known strategy is the
1206:Similar to the straddle is the
1164:Payoffs from selling a straddle
1136:CBOE S&P 500 PutWrite Index
297:Over-the-counter (off-exchange)
4721:Year-on-year inflation-indexed
4007:(2nd ed.), Indianapolis:
3786:Crack, Timothy Falcon (2004),
3750:Journal of Financial Economics
3298:
3287:, Options Clearing Corporation
3237:
3213:
3176:
3167:
3158:
3132:
3040:Chicago Board Options Exchange
2290:
2275:
2269:
2254:
2212:
2200:
2034:partial differential equations
1967:binomial options pricing model
1943:Binomial options pricing model
1269:According to the delivery type
1256:According to the option rights
816:the quantity and class of the
771:Chicago Board Options Exchange
682:mathematician and philosopher
13:
1:
4731:Zero-coupon inflation-indexed
4037:(Second ed.). New York.
3995:"Futures and Options Markets"
3411:"Understanding Stock Options"
3310:, Chicago Mercantile Exchange
3126:
3010:of Japan. It is owned by the
1850:Heath–Jarrow–Morton framework
1808:Heath–Jarrow–Morton framework
1475:Heath–Jarrow–Morton framework
1369:These are often described as
1099:
1029:Basic trades (American style)
989:futures and options exchanges
523:Sustainable development goals
3943:Journal of Political Economy
3555:Journal of Political Economy
3496:Journal of Political Economy
3085:Options Clearing Corporation
2091:
1983:and hybrid instruments, see
1826:interest rate cap and floors
1644:Stochastic volatility models
1416:
1120:
1040:
909:Options on futures contracts
884:Options Clearing Corporation
7:
4934:Foreign exchange derivative
4326:Callable bull/bear contract
4033:Natenberg, Sheldon (2015).
3647:Bruno Dupire (July 2007) .
3473:"Options pre-Black Scholes"
3070:Philadelphia Stock Exchange
3030:Area yield options contract
3017:
2964:Philadelphia Stock Exchange
2944:electronic trading platform
2909:To limit risk, brokers use
2884:A special situation called
2873:
1937:Binomial tree pricing model
1861:Brace–Gatarek–Musiela model
1477:for interest rates, to the
1172:Payoffs from a covered call
1071:
915:Callable bull/bear contract
876:exchange-traded derivatives
10:
5062:
4089:The Journal of Derivatives
3984:Financial Analysts Journal
3775:, Prentice-Hall, Chapter 5
3442:Fabozzi, Frank J. (2002).
2998:Tokyo Stock Exchange (TSE)
2877:
2085:
2079:
2050:implicit finite difference
2046:explicit finite difference
2025:
1994:
1946:
1940:
1882:
1869:mortgage-backed securities
1805:
1799:
1653:
1647:
1596:
1578:an estimate of the future
1531:
1426:
1420:
1337:
1145:
1108:Payoff from writing a call
903:Stock market index options
809:) or the right to sell (a
789:, or simply, derivatives.
698:describes the trading of "
674:Historical uses of options
668:
625:Definition and application
29:
5008:
4967:
4886:
4843:
4835:Stock market index future
4739:
4616:
4524:
4387:
4296:
4233:
4167:
4158:
4149:
3946:, 81 (3), 637–654 (1973).
3558:, 81 (3), 637–654 (1973).
3008:Financial Services Agency
2330:Standard hedge parameters
1834:interest rate derivatives
1129:Payoff from writing a put
1049:Payoff from buying a call
905:or, simply, index options
593:on or before a specified
406:Diversification (finance)
4954:Mortgage-backed security
4949:Interest rate derivative
4924:Equity-linked note (ELN)
4909:Credit-linked note (CLN)
3974:(also available online:
3952:The Journal of Investing
3184:Confusión de Confusiones
2680:{\displaystyle -\Delta }
2634:{\displaystyle d\sigma }
2562:{\displaystyle d\sigma }
2075:
2022:Finite difference models
1603:Following early work by
1247:
1080:Payoff from buying a put
929:Over-the-counter options
4904:Contract for difference
4205:Risk-free interest rate
3196:Smith, B. Mark (2003),
3025:American Stock Exchange
2905:Options approval levels
2512:{\displaystyle \theta }
2492:{\displaystyle \kappa }
2472:{\displaystyle \Gamma }
2452:{\displaystyle \Delta }
2171:{\displaystyle \theta }
2151:{\displaystyle \kappa }
2131:{\displaystyle \Gamma }
2111:{\displaystyle \Delta }
2042:finite difference model
2016:American styled options
1985:Lattice model (finance)
1949:Lattice model (finance)
1931:Bjerksund and Stensland
1927:Barone-Adesi and Whaley
1919:Roll–Geske–Whaley model
1512:The second part is the
870:Exchange-traded options
793:Contract specifications
696:Confusion of Confusions
4686:Forward Rate Agreement
4068:The Journal of Indexes
3914:"Japan Exchange Group"
3838:Baker, Howard (2023).
3649:"Pricing with a Smile"
3596:Hull, John C. (2005),
3568:Das, Satyajit (2006),
3379:Harris, Larry (2003),
3244:Hull, John C. (2005),
2862:
2705:
2681:
2658:
2635:
2612:
2586:
2563:
2540:
2513:
2493:
2473:
2453:
2425:
2303:
2172:
2152:
2132:
2112:
2070:finite element methods
2038:Black–Scholes equation
1766:
1746:
1702:SABR volatility models
1501:The first part is the
1316:employee stock options
1173:
1165:
1157:
1130:
1109:
1081:
1050:
1025:
979:
969:employee stock options
925:
861:
371:Alternative investment
4914:Credit default option
4258:Employee stock option
3722:Fixed Income Analysis
3623:Jim Gatheral (2006),
3381:Trading and Exchanges
3105:Real options analysis
3002:Founded in 1878, the
2958:Founded in 1790, The
2863:
2706:
2682:
2659:
2636:
2613:
2587:
2564:
2541:
2514:
2494:
2474:
2454:
2426:
2304:
2173:
2153:
2133:
2113:
2086:Further information:
2054:Crank–Nicolson method
1947:Further information:
1903:closed form solutions
1883:Further information:
1812:For the valuation of
1767:
1747:
1745:{\displaystyle S_{t}}
1694:#Risk-neutral_measure
1686:stochastic volatility
1684:, with the resultant
1650:Stochastic volatility
1473:for equities, to the
1237:(ticker symbol BXM).
1171:
1163:
1155:
1128:
1107:
1079:
1048:
1023:
977:
941:Interest rate options
923:
898:interest rate options
859:
780:. In contrast, other
657:transaction or on an
503:Investment management
416:Environmental finance
32:employee stock option
4868:Inflation derivative
4853:Commodity derivative
4825:Single-stock futures
4815:Normal backwardation
4805:Interest rate future
4646:Conditional variance
4152:Derivative (finance)
3918:Japan Exchange Group
3861:"Nasdaq PHLX (PHLX)"
3665:on September 7, 2012
3173:Aristotle. Politics.
3012:Japan Exchange Group
3004:Tokyo Stock Exchange
2962:, also known as the
2720:
2704:{\displaystyle \Pi }
2695:
2668:
2645:
2622:
2599:
2573:
2550:
2527:
2503:
2483:
2463:
2443:
2347:
2188:
2162:
2142:
2122:
2102:
1885:Valuation of options
1879:Model implementation
1756:
1729:
1692:as a prototype; see
1662:market crash of 1987
1629:Swedish Central Bank
1534:Valuation of options
1423:Valuation of options
765:Modern stock options
5020:Business portal
4873:Property derivative
3991:Millman, Gregory J.
3686:"Riding on a Smile"
3398:Law & Valuation
3330:ISE Traded Products
3221:Brealey, Richard A.
1907:Black–Scholes model
1893:Analytic techniques
1774:Black–Scholes model
1599:Black–Scholes model
1548:Black–Scholes model
1544:stochastic calculus
1493:Basic decomposition
1471:Black–Scholes model
1320:real estate options
787:derivative products
597:, depending on the
528:Sustainable finance
42:Part of a series on
4878:Weather derivative
4863:Freight derivative
4845:Exotic derivatives
4765:Commodities future
4452:Intermarket spread
4215:Synthetic position
4143:Derivatives market
3999:David R. Henderson
3307:Trade CME Products
3182:Josef de la Vega.
3115:Pin risk (options)
3080:Options backdating
2967:the U.S. In 2008,
2858:
2701:
2677:
2657:{\displaystyle dt}
2654:
2631:
2611:{\displaystyle dS}
2608:
2585:{\displaystyle dt}
2582:
2559:
2539:{\displaystyle dS}
2536:
2509:
2489:
2469:
2449:
2421:
2299:
2168:
2148:
2128:
2108:
1991:Monte Carlo models
1899:mathematical model
1762:
1742:
1675:volatility surface
1666:implied volatility
1607:and later work by
1542:pricing and using
1310:Other option types
1178:options strategies
1174:
1166:
1158:
1142:Options strategies
1131:
1110:
1082:
1051:
1026:
980:
926:
862:
518:Speculative attack
283:Structured product
5041:Options (finance)
5028:
5027:
4929:Equity derivative
4919:Credit derivative
4887:Other derivatives
4858:Energy derivative
4820:Perpetual futures
4701:Overnight indexed
4651:Constant maturity
4612:
4611:
4559:Finite difference
4492:Protective option
4101:978-3-486-58632-9
4044:978-0-07-181877-3
4018:978-0-86597-665-8
3849:. pp. 20–23.
3634:978-0-471-79251-2
3627:, Wiley Finance,
3583:978-0-273-70474-4
3045:Dilutive security
2926:Options exchanges
2899:counterparty risk
2893:Counterparty risk
2831:
2767:
2394:
2320:
2319:
2244:
2036:(see for example
2012:expectation value
1830:short-rate models
1820:(i.e. options on
1796:Short-rate models
1765:{\displaystyle t}
1706:numerical methods
1456:option time value
965:secondary markets
778:options exchanges
684:Thales of Miletus
610:market volatility
564:
563:
391:Banks and banking
381:Asset (economics)
207:Credit derivative
175:Stock certificate
48:Financial markets
16:(Redirected from
5053:
5018:
5017:
4790:Forwards pricing
4564:Garman–Kohlhagen
4165:
4164:
4136:
4129:
4122:
4113:
4112:
4062:
4056:
4048:
4029:
3955:, (Summer 2005).
3929:
3928:
3926:
3924:
3910:
3904:
3903:
3901:
3899:
3885:
3879:
3878:
3871:
3865:
3864:
3857:
3851:
3850:
3844:
3835:
3829:
3828:
3826:
3824:
3819:. March 18, 2015
3809:
3803:
3802:
3783:
3777:
3776:
3769:Rubinstein, Mark
3761:
3755:
3735:
3729:
3718:
3712:
3711:
3709:
3707:
3702:on July 10, 2011
3701:
3690:
3681:
3675:
3674:
3672:
3670:
3664:
3658:. Archived from
3653:
3644:
3638:
3637:
3620:
3611:
3610:
3593:
3587:
3586:
3575:
3565:
3559:
3550:
3544:
3543:
3535:
3529:
3528:
3490:
3484:
3483:
3477:
3471:Benhamou, Eric.
3468:
3462:
3461:
3446:(1st ed.).
3439:
3433:
3432:
3430:
3428:
3415:
3407:
3401:
3391:
3385:
3384:
3376:
3370:
3369:
3368:
3366:
3352:
3346:
3345:
3344:
3342:
3325:
3319:
3318:
3317:
3315:
3302:
3296:
3295:
3294:
3292:
3279:
3273:
3272:
3271:
3269:
3264:on July 29, 2016
3260:, archived from
3241:
3235:
3234:
3217:
3211:
3210:
3193:
3187:
3180:
3174:
3171:
3165:
3162:
3156:
3155:
3153:
3151:
3136:
3095:Options strategy
2867:
2865:
2864:
2859:
2832:
2827:
2826:
2825:
2812:
2768:
2763:
2762:
2761:
2748:
2710:
2708:
2707:
2702:
2686:
2684:
2683:
2678:
2663:
2661:
2660:
2655:
2640:
2638:
2637:
2632:
2617:
2615:
2614:
2609:
2591:
2589:
2588:
2583:
2568:
2566:
2565:
2560:
2545:
2543:
2542:
2537:
2518:
2516:
2515:
2510:
2498:
2496:
2495:
2490:
2478:
2476:
2475:
2470:
2458:
2456:
2455:
2450:
2430:
2428:
2427:
2422:
2395:
2390:
2389:
2388:
2375:
2308:
2306:
2305:
2300:
2250:
2246:
2245:
2240:
2239:
2230:
2177:
2175:
2174:
2169:
2157:
2155:
2154:
2149:
2137:
2135:
2134:
2129:
2117:
2115:
2114:
2109:
2092:
2060:in closed form.
1976:American options
1923:American options
1838:Black-Derman-Toy
1802:Short-rate model
1792:for discussion.
1771:
1769:
1768:
1763:
1751:
1749:
1748:
1743:
1741:
1740:
1719:is treated as a
1713:local volatility
1671:volatility smile
1656:Local volatility
1622:hedge parameters
1609:Robert C. Merton
1552:volatility smile
1528:Valuation models
1444:rational pricing
1299:Commodity option
1233:strategy is the
1148:Options strategy
983:Exchange trading
934:Over-the-counter
865:Forms of trading
842:settlement terms
782:over-the-counter
659:options exchange
655:over-the-counter
651:secondary market
618:over-the-counter
601:of the option.
556:
549:
542:
498:Impact investing
493:Growth investing
226:Foreign exchange
212:Futures exchange
160:Registered share
58:
39:
38:
21:
5061:
5060:
5056:
5055:
5054:
5052:
5051:
5050:
5031:
5030:
5029:
5024:
5012:
5004:
4990:Great Recession
4985:Government debt
4963:
4939:Fund derivative
4882:
4839:
4800:Futures pricing
4775:Dividend future
4770:Currency future
4753:
4735:
4608:
4584:Put–call parity
4520:
4507:Vertical spread
4442:Diagonal spread
4412:Calendar spread
4383:
4292:
4229:
4154:
4145:
4140:
4050:
4049:
4045:
4019:
3959:Kleinert, Hagen
3937:
3935:Further reading
3932:
3922:
3920:
3912:
3911:
3907:
3897:
3895:
3887:
3886:
3882:
3873:
3872:
3868:
3859:
3858:
3854:
3842:
3836:
3832:
3822:
3820:
3811:
3810:
3806:
3800:
3784:
3780:
3773:Options Markets
3762:
3758:
3736:
3732:
3719:
3715:
3705:
3703:
3699:
3688:
3682:
3678:
3668:
3666:
3662:
3651:
3645:
3641:
3635:
3621:
3614:
3608:
3594:
3590:
3584:
3566:
3562:
3551:
3547:
3536:
3532:
3491:
3487:
3475:
3469:
3465:
3458:
3440:
3436:
3426:
3424:
3413:
3409:
3408:
3404:
3392:
3388:
3377:
3373:
3364:
3362:
3353:
3349:
3340:
3338:
3337:on May 11, 2007
3327:
3326:
3322:
3313:
3311:
3304:
3303:
3299:
3290:
3288:
3281:
3280:
3276:
3267:
3265:
3258:
3242:
3238:
3218:
3214:
3208:
3194:
3190:
3181:
3177:
3172:
3168:
3163:
3159:
3149:
3147:
3137:
3133:
3129:
3124:
3075:LEAPS (finance)
3035:Ascot (finance)
3020:
3000:
2988:
2977:
2960:NASDAQ OMX PHLX
2956:
2954:NASDAQ OMX PHLX
2933:
2928:
2907:
2895:
2882:
2876:
2821:
2817:
2813:
2811:
2757:
2753:
2749:
2747:
2721:
2718:
2717:
2696:
2693:
2692:
2669:
2666:
2665:
2646:
2643:
2642:
2623:
2620:
2619:
2600:
2597:
2596:
2574:
2571:
2570:
2551:
2548:
2547:
2528:
2525:
2524:
2504:
2501:
2500:
2484:
2481:
2480:
2464:
2461:
2460:
2444:
2441:
2440:
2384:
2380:
2376:
2374:
2348:
2345:
2344:
2332:
2235:
2231:
2229:
2222:
2218:
2189:
2186:
2185:
2163:
2160:
2159:
2143:
2140:
2139:
2123:
2120:
2119:
2103:
2100:
2099:
2090:
2084:
2078:
2066:
2030:
2024:
1999:
1993:
1963:Mark Rubinstein
1951:
1945:
1939:
1917:. Although the
1895:
1887:
1881:
1810:
1804:
1798:
1757:
1754:
1753:
1736:
1732:
1730:
1727:
1726:
1688:models and the
1658:
1652:
1646:
1605:Louis Bachelier
1601:
1595:
1536:
1530:
1503:intrinsic value
1495:
1460:put–call parity
1448:risk neutrality
1439:
1425:
1419:
1342:
1336:
1312:
1302:Currency option
1284:
1271:
1258:
1250:
1227:put–call parity
1150:
1144:
1123:
1102:
1074:
1043:
1031:
997:price discovery
985:
931:
872:
867:
854:
795:
767:
744:Lines of credit
731:earnest payment
676:
671:
653:, in either an
627:
589:at a specified
560:
401:Climate finance
330:
316:
244:
243:
223:
222:
217:Hybrid security
155:Preferred stock
125:
116:High-yield debt
111:Government bond
35:
28:
23:
22:
15:
12:
11:
5:
5059:
5049:
5048:
5043:
5026:
5025:
5023:
5022:
5009:
5006:
5005:
5003:
5002:
4997:
4995:Municipal debt
4992:
4987:
4982:
4980:Corporate debt
4977:
4971:
4969:
4965:
4964:
4962:
4961:
4956:
4951:
4946:
4941:
4936:
4931:
4926:
4921:
4916:
4911:
4906:
4901:
4896:
4890:
4888:
4884:
4883:
4881:
4880:
4875:
4870:
4865:
4860:
4855:
4849:
4847:
4841:
4840:
4838:
4837:
4832:
4827:
4822:
4817:
4812:
4807:
4802:
4797:
4792:
4787:
4782:
4780:Forward market
4777:
4772:
4767:
4762:
4756:
4754:
4752:
4751:
4746:
4740:
4737:
4736:
4734:
4733:
4728:
4723:
4718:
4713:
4708:
4703:
4698:
4693:
4688:
4683:
4678:
4673:
4668:
4663:
4661:Credit default
4658:
4653:
4648:
4643:
4638:
4633:
4628:
4622:
4620:
4614:
4613:
4610:
4609:
4607:
4606:
4601:
4596:
4591:
4586:
4581:
4576:
4571:
4566:
4561:
4556:
4546:
4541:
4536:
4530:
4528:
4522:
4521:
4519:
4518:
4504:
4499:
4494:
4489:
4484:
4479:
4474:
4469:
4464:
4459:
4457:Iron butterfly
4454:
4449:
4444:
4439:
4434:
4429:
4427:Covered option
4424:
4419:
4414:
4409:
4404:
4399:
4393:
4391:
4385:
4384:
4382:
4381:
4376:
4371:
4366:
4365:Mountain range
4363:
4358:
4353:
4348:
4343:
4338:
4333:
4328:
4323:
4318:
4313:
4308:
4302:
4300:
4294:
4293:
4291:
4290:
4285:
4280:
4275:
4270:
4265:
4260:
4255:
4250:
4245:
4239:
4237:
4231:
4230:
4228:
4227:
4222:
4217:
4212:
4207:
4202:
4197:
4192:
4187:
4182:
4177:
4171:
4169:
4162:
4156:
4155:
4150:
4147:
4146:
4139:
4138:
4131:
4124:
4116:
4110:
4109:
4103:
4093:
4084:
4075:
4072:
4063:
4043:
4030:
4017:
3987:
3980:
3956:
3947:
3936:
3933:
3931:
3930:
3905:
3880:
3866:
3852:
3830:
3804:
3798:
3778:
3756:
3730:
3713:
3676:
3639:
3633:
3612:
3606:
3588:
3582:
3560:
3545:
3530:
3509:10.1086/260062
3503:(3): 637–654.
3485:
3463:
3456:
3434:
3402:
3386:
3371:
3347:
3320:
3297:
3274:
3256:
3236:
3225:Myers, Stewart
3212:
3206:
3188:
3175:
3166:
3157:
3130:
3128:
3125:
3123:
3122:
3117:
3112:
3107:
3102:
3097:
3092:
3090:Options spread
3087:
3082:
3077:
3072:
3067:
3062:
3057:
3055:Euronext.liffe
3052:
3047:
3042:
3037:
3032:
3027:
3021:
3019:
3016:
2999:
2996:
2991:Eurex Exchange
2987:
2986:Eurex Exchange
2984:
2976:
2973:
2955:
2952:
2932:
2929:
2927:
2924:
2911:access control
2906:
2903:
2894:
2891:
2878:Main article:
2875:
2872:
2871:
2870:
2869:
2868:
2856:
2853:
2850:
2847:
2844:
2841:
2838:
2835:
2830:
2824:
2820:
2816:
2810:
2807:
2804:
2801:
2798:
2795:
2792:
2789:
2786:
2783:
2780:
2777:
2774:
2771:
2766:
2760:
2756:
2752:
2746:
2743:
2740:
2737:
2734:
2731:
2728:
2725:
2700:
2676:
2673:
2653:
2650:
2630:
2627:
2607:
2604:
2581:
2578:
2558:
2555:
2535:
2532:
2508:
2488:
2468:
2448:
2434:
2433:
2432:
2431:
2419:
2416:
2413:
2410:
2407:
2404:
2401:
2398:
2393:
2387:
2383:
2379:
2373:
2370:
2367:
2364:
2361:
2358:
2355:
2352:
2331:
2328:
2318:
2317:
2312:
2311:
2310:
2309:
2298:
2295:
2292:
2289:
2286:
2283:
2280:
2277:
2274:
2271:
2268:
2265:
2262:
2259:
2256:
2253:
2249:
2243:
2238:
2234:
2228:
2225:
2221:
2217:
2214:
2211:
2208:
2205:
2202:
2199:
2196:
2193:
2167:
2147:
2127:
2107:
2077:
2074:
2065:
2062:
2026:Main article:
2023:
2020:
1995:Main article:
1992:
1989:
1980:trinomial tree
1941:Main article:
1938:
1935:
1894:
1891:
1880:
1877:
1846:interest rates
1800:Main article:
1797:
1794:
1782:Emanuel Derman
1761:
1739:
1735:
1648:Main article:
1645:
1642:
1631:'s associated
1597:Main article:
1594:
1591:
1584:
1583:
1576:
1569:
1566:
1559:
1532:Main article:
1529:
1526:
1525:
1524:
1521:expected value
1510:
1494:
1491:
1421:Main article:
1418:
1415:
1414:
1413:
1405:
1397:
1389:
1381:
1367:
1366:
1360:
1338:Main article:
1335:
1332:
1328:mortgage loans
1311:
1308:
1307:
1306:
1303:
1300:
1297:
1294:
1291:
1288:
1283:
1280:
1279:
1278:
1275:
1270:
1267:
1266:
1265:
1262:
1257:
1254:
1249:
1246:
1242:protective put
1146:Main article:
1143:
1140:
1138:(ticker PUT).
1122:
1119:
1101:
1098:
1073:
1070:
1042:
1039:
1030:
1027:
1018:
1017:
1014:
1011:
1008:
984:
981:
957:
956:
945:
942:
930:
927:
918:
917:
912:
906:
900:
891:
880:clearing house
871:
868:
866:
863:
853:
852:Option trading
850:
849:
848:
845:
838:
831:
821:
814:
794:
791:
766:
763:
694:The 1688 book
691:his 'option'.
675:
672:
670:
667:
626:
623:
562:
561:
559:
558:
551:
544:
536:
533:
532:
531:
530:
525:
520:
515:
510:
505:
500:
495:
490:
485:
480:
479:
478:
473:
468:
463:
458:
453:
448:
443:
438:
433:
423:
418:
413:
408:
403:
398:
393:
388:
383:
378:
376:Angel investor
373:
365:
364:
360:
359:
358:
357:
352:
347:
339:
338:
332:
331:
329:
328:
323:
317:
315:
314:
309:
303:
300:
299:
293:
292:
291:
290:
288:Swap (finance)
285:
280:
275:
270:
265:
260:
255:
250:
242:
241:
235:
228:
224:
221:
220:
214:
209:
202:
198:
195:
194:
190:
189:
188:
187:
182:
180:Stock exchange
177:
172:
167:
162:
157:
152:
147:
139:
138:
132:
131:
130:
129:
127:Securitization
123:
121:Municipal bond
118:
113:
108:
103:
101:Corporate bond
98:
96:Bond valuation
90:
89:
83:
82:
81:
80:
68:
60:
59:
51:
50:
44:
43:
26:
18:Vanilla option
9:
6:
4:
3:
2:
5058:
5047:
5044:
5042:
5039:
5038:
5036:
5021:
5016:
5011:
5010:
5007:
5001:
4998:
4996:
4993:
4991:
4988:
4986:
4983:
4981:
4978:
4976:
4975:Consumer debt
4973:
4972:
4970:
4968:Market issues
4966:
4960:
4957:
4955:
4952:
4950:
4947:
4945:
4944:Fund of funds
4942:
4940:
4937:
4935:
4932:
4930:
4927:
4925:
4922:
4920:
4917:
4915:
4912:
4910:
4907:
4905:
4902:
4900:
4897:
4895:
4892:
4891:
4889:
4885:
4879:
4876:
4874:
4871:
4869:
4866:
4864:
4861:
4859:
4856:
4854:
4851:
4850:
4848:
4846:
4842:
4836:
4833:
4831:
4828:
4826:
4823:
4821:
4818:
4816:
4813:
4811:
4808:
4806:
4803:
4801:
4798:
4796:
4793:
4791:
4788:
4786:
4785:Forward price
4783:
4781:
4778:
4776:
4773:
4771:
4768:
4766:
4763:
4761:
4758:
4757:
4755:
4750:
4747:
4745:
4742:
4741:
4738:
4732:
4729:
4727:
4724:
4722:
4719:
4717:
4714:
4712:
4709:
4707:
4704:
4702:
4699:
4697:
4696:Interest rate
4694:
4692:
4689:
4687:
4684:
4682:
4679:
4677:
4674:
4672:
4669:
4667:
4664:
4662:
4659:
4657:
4654:
4652:
4649:
4647:
4644:
4642:
4639:
4637:
4634:
4632:
4629:
4627:
4624:
4623:
4621:
4619:
4615:
4605:
4602:
4600:
4597:
4595:
4592:
4590:
4589:MC Simulation
4587:
4585:
4582:
4580:
4577:
4575:
4572:
4570:
4567:
4565:
4562:
4560:
4557:
4554:
4550:
4549:Black–Scholes
4547:
4545:
4542:
4540:
4537:
4535:
4532:
4531:
4529:
4527:
4523:
4516:
4512:
4508:
4505:
4503:
4502:Risk reversal
4500:
4498:
4495:
4493:
4490:
4488:
4485:
4483:
4480:
4478:
4475:
4473:
4470:
4468:
4465:
4463:
4460:
4458:
4455:
4453:
4450:
4448:
4445:
4443:
4440:
4438:
4435:
4433:
4432:Credit spread
4430:
4428:
4425:
4423:
4420:
4418:
4415:
4413:
4410:
4408:
4405:
4403:
4400:
4398:
4395:
4394:
4392:
4390:
4386:
4380:
4377:
4375:
4372:
4370:
4367:
4364:
4362:
4359:
4357:
4356:Interest rate
4354:
4352:
4351:Forward start
4349:
4347:
4344:
4342:
4339:
4337:
4334:
4332:
4329:
4327:
4324:
4322:
4319:
4317:
4314:
4312:
4309:
4307:
4304:
4303:
4301:
4299:
4295:
4289:
4286:
4284:
4281:
4279:
4278:Option styles
4276:
4274:
4271:
4269:
4266:
4264:
4261:
4259:
4256:
4254:
4251:
4249:
4246:
4244:
4241:
4240:
4238:
4236:
4232:
4226:
4223:
4221:
4218:
4216:
4213:
4211:
4208:
4206:
4203:
4201:
4198:
4196:
4195:Open interest
4193:
4191:
4188:
4186:
4183:
4181:
4178:
4176:
4175:Delta neutral
4173:
4172:
4170:
4166:
4163:
4161:
4157:
4153:
4148:
4144:
4137:
4132:
4130:
4125:
4123:
4118:
4117:
4114:
4108:
4104:
4102:
4098:
4094:
4091:
4090:
4085:
4082:
4081:
4076:
4073:
4070:
4069:
4064:
4060:
4054:
4046:
4040:
4036:
4031:
4028:
4024:
4020:
4014:
4010:
4006:
4005:
4000:
3996:
3992:
3988:
3985:
3981:
3979:
3977:
3972:
3971:981-238-107-4
3968:
3964:
3960:
3957:
3954:
3953:
3948:
3945:
3944:
3939:
3938:
3919:
3915:
3909:
3894:
3893:www.eurex.com
3890:
3884:
3876:
3870:
3862:
3856:
3848:
3841:
3834:
3818:
3814:
3808:
3801:
3799:0-9700552-2-6
3795:
3791:
3790:
3782:
3774:
3770:
3766:
3760:
3754:
3751:
3747:
3743:
3739:
3734:
3728:
3725:, p. 410, at
3724:
3723:
3717:
3698:
3694:
3687:
3680:
3661:
3657:
3650:
3643:
3636:
3630:
3626:
3619:
3617:
3609:
3607:0-13-149908-4
3603:
3599:
3592:
3585:
3579:
3574:
3573:
3564:
3557:
3556:
3549:
3541:
3534:
3526:
3522:
3518:
3514:
3510:
3506:
3502:
3498:
3497:
3489:
3481:
3480:Eric Benhamou
3474:
3467:
3459:
3457:0-471-22092-2
3453:
3449:
3445:
3438:
3423:
3419:
3412:
3406:
3399:
3395:
3390:
3382:
3375:
3360:
3359:
3351:
3336:
3332:
3331:
3324:
3309:
3308:
3301:
3286:
3285:
3278:
3263:
3259:
3257:0-13-149908-4
3253:
3249:
3248:
3240:
3232:
3231:
3226:
3222:
3216:
3209:
3207:0-226-76404-4
3203:
3199:
3192:
3185:
3179:
3170:
3161:
3146:
3142:
3135:
3131:
3121:
3118:
3116:
3113:
3111:
3110:PnL Explained
3108:
3106:
3103:
3101:
3100:Option symbol
3098:
3096:
3093:
3091:
3088:
3086:
3083:
3081:
3078:
3076:
3073:
3071:
3068:
3066:
3063:
3061:
3058:
3056:
3053:
3051:
3048:
3046:
3043:
3041:
3038:
3036:
3033:
3031:
3028:
3026:
3023:
3022:
3015:
3013:
3009:
3005:
2995:
2992:
2983:
2981:
2972:
2970:
2965:
2961:
2951:
2949:
2945:
2941:
2937:
2923:
2921:
2917:
2912:
2902:
2900:
2890:
2887:
2881:
2854:
2851:
2848:
2845:
2842:
2839:
2836:
2833:
2828:
2822:
2818:
2814:
2805:
2802:
2799:
2793:
2790:
2787:
2784:
2781:
2778:
2775:
2772:
2769:
2764:
2758:
2754:
2750:
2741:
2738:
2735:
2729:
2723:
2716:
2715:
2714:
2713:
2712:
2690:
2689:delta neutral
2671:
2651:
2648:
2628:
2625:
2605:
2602:
2593:
2579:
2576:
2556:
2553:
2533:
2530:
2522:
2521:Black–Scholes
2506:
2486:
2439:
2417:
2414:
2411:
2408:
2405:
2402:
2399:
2396:
2391:
2385:
2381:
2377:
2368:
2365:
2362:
2356:
2353:
2350:
2343:
2342:
2341:
2340:
2339:
2337:
2327:
2325:
2316:
2296:
2293:
2287:
2284:
2281:
2278:
2272:
2266:
2263:
2260:
2257:
2251:
2247:
2241:
2236:
2232:
2226:
2223:
2219:
2215:
2209:
2206:
2203:
2197:
2194:
2191:
2184:
2183:
2182:
2181:
2180:
2165:
2145:
2094:
2093:
2089:
2083:
2073:
2071:
2061:
2059:
2055:
2051:
2047:
2043:
2039:
2035:
2029:
2019:
2017:
2013:
2009:
2004:
1998:
1988:
1986:
1981:
1977:
1972:
1971:discrete time
1968:
1964:
1960:
1956:
1950:
1944:
1934:
1932:
1928:
1924:
1920:
1916:
1912:
1908:
1904:
1900:
1890:
1886:
1876:
1874:
1870:
1866:
1865:market models
1862:
1858:
1855:
1851:
1847:
1843:
1839:
1835:
1831:
1827:
1823:
1819:
1815:
1809:
1803:
1793:
1791:
1787:
1783:
1779:
1775:
1759:
1737:
1733:
1724:
1723:
1722:deterministic
1718:
1715:model, where
1714:
1709:
1707:
1703:
1699:
1695:
1691:
1687:
1683:
1678:
1676:
1672:
1667:
1663:
1657:
1651:
1641:
1638:
1635:(a.k.a., the
1634:
1630:
1625:
1623:
1618:
1617:Myron Scholes
1614:
1613:Fischer Black
1610:
1606:
1600:
1593:Black–Scholes
1590:
1587:
1581:
1577:
1574:
1570:
1567:
1564:
1560:
1557:
1556:
1555:
1553:
1549:
1545:
1541:
1535:
1522:
1519:
1515:
1511:
1508:
1504:
1500:
1499:
1498:
1490:
1488:
1487:Asset pricing
1484:
1480:
1476:
1472:
1468:
1463:
1461:
1457:
1453:
1449:
1445:
1438:
1434:
1430:
1424:
1411:
1410:
1406:
1403:
1402:
1398:
1395:
1394:
1390:
1387:
1386:
1382:
1379:
1376:
1375:
1374:
1372:
1364:
1361:
1358:
1354:
1350:
1347:
1346:
1345:
1341:
1334:Option styles
1331:
1329:
1325:
1321:
1317:
1304:
1301:
1298:
1295:
1293:Future option
1292:
1289:
1287:Equity option
1286:
1285:
1276:
1273:
1272:
1263:
1260:
1259:
1253:
1245:
1243:
1238:
1236:
1232:
1228:
1224:
1220:
1216:
1211:
1209:
1204:
1202:
1197:
1194:
1189:
1186:
1181:
1179:
1170:
1162:
1154:
1149:
1139:
1137:
1127:
1118:
1115:
1106:
1097:
1095:
1090:
1087:
1078:
1069:
1066:
1062:
1060:
1056:
1047:
1038:
1036:
1022:
1015:
1012:
1009:
1006:
1002:
1001:
1000:
998:
994:
993:ticker symbol
990:
976:
972:
970:
966:
961:
954:
950:
946:
943:
940:
939:
938:
935:
922:
916:
913:
910:
907:
904:
901:
899:
895:
892:
890:Stock options
889:
888:
887:
885:
881:
877:
858:
846:
843:
839:
836:
832:
830:
826:
822:
819:
815:
812:
808:
804:
803:
802:
800:
790:
788:
783:
779:
774:
772:
762:
760:
756:
752:
747:
745:
741:
739:
734:
732:
728:
723:
718:
716:
712:
707:
705:
701:
697:
692:
689:
685:
681:
680:ancient Greek
666:
664:
660:
656:
652:
647:
643:
641:
637:
633:
622:
620:
619:
613:
611:
607:
602:
600:
596:
592:
588:
584:
581:
577:
573:
569:
557:
552:
550:
545:
543:
538:
537:
535:
534:
529:
526:
524:
521:
519:
516:
514:
511:
509:
506:
504:
501:
499:
496:
494:
491:
489:
486:
484:
481:
477:
474:
472:
469:
467:
464:
462:
459:
457:
454:
452:
449:
447:
444:
442:
439:
437:
434:
432:
429:
428:
427:
424:
422:
419:
417:
414:
412:
411:Eco-investing
409:
407:
404:
402:
399:
397:
394:
392:
389:
387:
386:Asset pricing
384:
382:
379:
377:
374:
372:
369:
368:
367:
366:
363:Related areas
362:
361:
356:
353:
351:
348:
346:
343:
342:
341:
340:
337:
334:
333:
327:
324:
322:
319:
318:
313:
310:
308:
305:
304:
302:
301:
298:
295:
294:
289:
286:
284:
281:
279:
276:
274:
271:
269:
266:
264:
261:
259:
256:
254:
251:
249:
246:
245:
239:
238:Exchange rate
236:
234:
230:
229:
227:
218:
215:
213:
210:
208:
204:
203:
201:
197:
196:
193:Other markets
192:
191:
186:
185:Watered stock
183:
181:
178:
176:
173:
171:
168:
166:
163:
161:
158:
156:
153:
151:
148:
146:
143:
142:
141:
140:
137:
134:
133:
128:
124:
122:
119:
117:
114:
112:
109:
107:
104:
102:
99:
97:
94:
93:
92:
91:
88:
85:
84:
79:
76:
72:
69:
67:
66:Public market
64:
63:
62:
61:
57:
53:
52:
49:
46:
45:
41:
40:
37:
33:
19:
5046:Contract law
4795:Forward rate
4706:Total return
4594:Real options
4497:Ratio spread
4477:Naked option
4437:Debit spread
4268:Fixed income
4210:Strike price
4159:
4087:
4078:
4066:
4034:
4002:
3973:
3962:
3951:
3941:
3921:. Retrieved
3917:
3908:
3896:. Retrieved
3892:
3883:
3869:
3855:
3846:
3833:
3821:. Retrieved
3807:
3788:
3781:
3772:
3765:Cox, John C.
3759:
3752:, 7:229–263.
3746:Rubinstein M
3733:
3727:Google Books
3720:
3716:
3704:. Retrieved
3697:the original
3692:
3679:
3667:. Retrieved
3660:the original
3655:
3642:
3624:
3597:
3591:
3571:
3563:
3554:
3548:
3539:
3533:
3500:
3494:
3488:
3479:
3466:
3443:
3437:
3425:. Retrieved
3405:
3389:
3380:
3374:
3363:, retrieved
3357:
3350:
3339:, retrieved
3335:the original
3329:
3323:
3312:, retrieved
3306:
3300:
3289:, retrieved
3283:
3277:
3266:, retrieved
3262:the original
3246:
3239:
3229:
3215:
3197:
3191:
3183:
3178:
3169:
3160:
3148:. Retrieved
3145:Investopedia
3144:
3134:
3001:
2989:
2978:
2957:
2934:
2908:
2896:
2883:
2594:
2435:
2333:
2321:
2313:
2096:
2067:
2064:Other models
2031:
2000:
1959:Stephen Ross
1952:
1933:and others.
1905:such as the
1896:
1888:
1853:
1814:bond options
1811:
1790:#Development
1778:Bruno Dupire
1752:and of time
1720:
1710:
1690:Heston model
1679:
1659:
1626:
1602:
1588:
1585:
1571:The time to
1563:strike price
1540:risk-neutral
1537:
1513:
1502:
1496:
1479:Heston model
1464:
1440:
1407:
1399:
1391:
1383:
1377:
1370:
1368:
1362:
1348:
1343:
1340:Option style
1313:
1296:Index option
1251:
1239:
1215:covered call
1212:
1205:
1198:
1190:
1182:
1175:
1132:
1111:
1091:
1083:
1067:
1063:
1059:strike price
1052:
1032:
986:
962:
958:
932:
894:Bond options
873:
825:strike price
796:
775:
768:
748:
742:
735:
719:
708:
699:
693:
677:
648:
644:
628:
616:
614:
603:
591:strike price
575:
571:
565:
513:Market trend
488:Greenwashing
345:Participants
311:
267:
150:Growth stock
145:Common stock
136:Stock market
106:Fixed income
74:
36:
4726:Zero Coupon
4656:Correlation
4604:Vanna–Volga
4462:Iron condor
4248:Bond option
2940:S&P 500
2916:naked calls
2336:Itô's lemma
2003:intractable
1911:Black model
1873:Black model
1857:yield curve
1637:Nobel Prize
1305:Swap option
1290:Bond option
1221:. See also
1055:call option
947:Options on
807:call option
755:convertible
729:account an
722:real estate
508:Market risk
321:Spot market
278:Reinsurance
273:Real estate
263:Mutual fund
200:Derivatives
170:Stockbroker
87:Bond market
5035:Categories
5000:Tax policy
4716:Volatility
4626:Amortising
4467:Jelly roll
4402:Box spread
4397:Backspread
4389:Strategies
4225:Volatility
4220:the Greeks
4185:Expiration
3889:"About us"
3823:August 27,
3738:Cox, J. C.
3448:New Jersey
3427:August 27,
3394:invest-faq
3127:References
2920:naked puts
2436:where the
2080:See also:
2008:simulation
1842:Hull–White
1806:See also:
1717:volatility
1682:stochastic
1660:Since the
1654:See also:
1580:volatility
1573:expiration
1518:discounted
1514:time value
1507:underlying
1483:stochastic
1427:See also:
1357:expiration
1324:prepayment
1219:naked call
1199:Selling a
1100:Short call
1086:put option
896:and other
835:expiration
818:underlying
811:put option
799:term sheet
632:spot price
587:instrument
580:underlying
350:Regulation
78:Securities
4691:Inflation
4641:Commodity
4599:Trinomial
4534:Bachelier
4526:Valuation
4407:Butterfly
4341:Commodore
4190:Moneyness
4053:cite book
4027:237794267
3976:PDF-files
3525:154552078
3268:April 21,
3065:NYSE Arca
2849:θ
2843:σ
2837:κ
2809:Γ
2797:Δ
2794:−
2785:θ
2779:σ
2773:κ
2745:Γ
2733:Δ
2727:Π
2699:Π
2675:Δ
2672:−
2629:σ
2557:σ
2507:θ
2487:κ
2467:Γ
2447:Δ
2412:θ
2406:σ
2400:κ
2372:Γ
2360:Δ
2285:⋅
2279:−
2264:−
2261:⋅
2227:⋅
2207:⋅
2166:θ
2146:κ
2126:Γ
2106:Δ
2095:Example:
2058:tractable
1818:swaptions
1786:Iraj Kani
1467:"process"
1452:moneyness
1417:Valuation
1353:exercised
1231:buy-write
1223:naked put
1185:butterfly
1121:Short put
1041:Long call
953:swaptions
606:valuation
451:corporate
426:Financial
248:Commodity
4830:Slippage
4760:Contango
4744:Forwards
4711:Variance
4671:Dividend
4666:Currency
4579:Margrabe
4574:Lattices
4553:equation
4539:Binomial
4487:Strangle
4482:Straddle
4379:Swaption
4361:Lookback
4346:Compound
4288:Warrants
4263:European
4243:American
4235:Vanillas
4200:Pin risk
4180:Exercise
3993:(2008),
3923:March 3,
3898:March 3,
3847:moaf.org
3771:(1985),
3669:June 14,
3365:June 19,
3341:June 21,
3314:June 21,
3291:July 15,
3227:(2003),
3018:See also
2886:pin risk
2880:Pin risk
2874:Pin risk
2052:and the
1955:John Cox
1915:"Greeks"
1909:and the
1378:Bermudan
1363:European
1349:American
1208:strangle
1201:straddle
1072:Long put
829:exercise
759:Mortgage
704:Euronext
663:dividend
476:services
466:personal
461:forecast
431:analysis
355:Clearing
307:Forwards
233:Currency
71:Exchange
4749:Futures
4369:Rainbow
4336:Cliquet
4331:Chooser
4311:Barrier
4298:Exotics
4160:Options
4001:(ed.),
3742:Ross SA
3706:June 1,
3517:1831029
3150:June 2,
2950:(SEC).
1824:), and
1393:Barrier
1371:vanilla
1094:shorted
1035:hedging
720:In the
711:William
669:History
568:finance
483:Fintech
446:betting
436:analyst
336:Trading
312:Options
4810:Margin
4676:Equity
4569:Heston
4472:Ladder
4422:Condor
4417:Collar
4374:Spread
4321:Binary
4316:Basket
4099:
4041:
4025:
4015:
3969:
3796:
3631:
3604:
3580:
3523:
3515:
3454:
3361:, CNet
3254:
3204:
2969:NASDAQ
2523:, and
2438:Greeks
2324:return
2297:0.0614
2224:0.0631
1854:entire
1485:. See
1458:, and
1446:(i.e.
1435:, and
1409:Exotic
1401:Binary
1193:condor
1007:(AAA),
1005:rating
727:escrow
700:opsies
576:holder
572:option
471:public
268:Option
73:
4681:Forex
4636:Basis
4631:Asset
4618:Swaps
4544:Black
4447:Fence
4306:Asian
4168:Terms
3997:, in
3843:(PDF)
3700:(PDF)
3689:(PDF)
3663:(PDF)
3652:(PDF)
3521:S2CID
3513:JSTOR
3476:(PDF)
3414:(PDF)
3050:Eurex
2282:0.022
2267:0.015
2204:0.439
2076:Risks
1822:swaps
1385:Asian
1248:Types
1114:short
949:swaps
688:olive
599:style
583:asset
570:, an
456:crime
441:asset
326:Swaps
258:Money
165:Stock
4515:Bull
4511:Bear
4253:Call
4097:ISBN
4059:link
4039:ISBN
4023:OCLC
4013:ISBN
3967:ISBN
3925:2024
3900:2024
3825:2022
3794:ISBN
3744:and
3708:2007
3671:2013
3656:Risk
3629:ISBN
3602:ISBN
3578:ISBN
3452:ISBN
3429:2015
3422:CBOE
3420:and
3367:2007
3343:2007
3316:2007
3293:2020
3270:2008
3252:ISBN
3202:ISBN
3152:2014
2918:and
2711:is:
2641:and
2569:and
2499:and
2338:as:
1961:and
1863:and
1840:and
1784:and
1780:and
1700:and
1615:and
1561:The
967:for
840:the
833:the
823:the
751:bond
715:Mary
713:and
636:call
595:date
396:Bull
4283:Put
3505:doi
3396:or
3120:XVA
2258:9.6
2233:0.5
2210:0.5
1698:CEV
1450:),
951:or
911:and
640:put
585:or
566:In
421:ESG
253:ETF
5037::
4513:,
4273:FX
4055:}}
4051:{{
4021:,
4011:,
3961:,
3916:.
3891:.
3845:.
3815:.
3767:;
3740:,
3691:.
3654:.
3615:^
3519:.
3511:.
3501:81
3499:.
3478:.
3416:.
3223:;
3143:.
3014:.
2618:,
2546:,
2479:,
2459:,
2158:,
2138:,
2118:,
2072:.
2048:,
1987:.
1957:,
1929:,
1816:,
1708:.
1677:.
1611:,
1462:.
1454:,
1431:,
1191:A
1096:.
665:.
642:.
4555:)
4551:(
4517:)
4509:(
4135:e
4128:t
4121:v
4061:)
4047:.
3978:)
3927:.
3902:.
3877:.
3863:.
3827:.
3710:.
3673:.
3527:.
3507::
3482:.
3460:.
3431:.
3154:.
2855:t
2852:d
2846:+
2840:d
2834:+
2829:2
2823:2
2819:S
2815:d
2806:=
2803:S
2800:d
2791:t
2788:d
2782:+
2776:d
2770:+
2765:2
2759:2
2755:S
2751:d
2742:+
2739:S
2736:d
2730:=
2724:d
2652:t
2649:d
2626:d
2606:S
2603:d
2580:t
2577:d
2554:d
2534:S
2531:d
2418:t
2415:d
2409:+
2403:d
2397:+
2392:2
2386:2
2382:S
2378:d
2369:+
2366:S
2363:d
2357:=
2354:C
2351:d
2294:=
2291:)
2288:1
2276:(
2273:+
2270:)
2255:(
2252:+
2248:)
2242:2
2237:2
2220:(
2216:+
2213:)
2201:(
2198:=
2195:C
2192:d
1760:t
1738:t
1734:S
1359:.
955:.
813:)
555:e
548:t
541:v
240:)
231:(
219:)
205:(
75:·
34:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.