Option (finance) - Knowledge

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.

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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.

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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).

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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:

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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.

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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

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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.

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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).

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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.

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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.

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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

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Bloss, Michael; Ernst, Dietmar; Häcker Joachim (2008): Derivatives – An authoritative guide to derivatives for financial intermediaries and investors Oldenbourg Verlag München

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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,

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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.

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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

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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

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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

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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

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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-

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portfolio that is hedged from loss for small changes in the underlying's price. The corresponding price sensitivity formula for this portfolio

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As with all securities, trading options entails the risk of the option's value changing over time. However, unlike traditional securities, the

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and execute transactions. As an intermediary to both sides of the transaction, the benefits the exchange provides to the transaction include:

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can be derived, and the valuation obtained. A number of implementations of finite difference methods exist for option valuation, including:

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Put options give the holder the right – but not the obligation – to sell something at a specific price for a specific time period.

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Call options give the holder the right – but not the obligation – to buy something at a specific price for a specific time period.

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Reilly, Frank and Keith C. Brown, Investment Analysis and Portfolio Management, 7th edition, Thompson Southwestern, 2003, pp. 994–5.

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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

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Strategies are often used to engineer a particular risk profile to movements in the underlying security. For example, buying a

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Hill, Joanne, Venkatesh Balasubramanian, Krag (Buzz) Gregory, and Ingrid Tierens. "Finding Alpha via Covered Index Writing".

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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

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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)

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As above, the value of the option is estimated using a variety of quantitative techniques, all based on the principle of

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Schneeweis, Thomas, and Richard Spurgin. "The Benefits of Index Option-Based Strategies for Institutional Portfolios"

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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.

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The trader exercising a put option on a stock does not need to own the underlying asset, because most stocks can be

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into common stock at the buyer's option, or may be called (bought back) at specified prices at the issuer's option.

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In London, puts and "refusals" (calls) first became well-known trading instruments in the 1690s during the reign of

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by describing the future evolution of the short rate. The other major framework for interest rate modelling is the

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Once a valuation model has been chosen, there are a number of different techniques used to implement the models.

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produced a closed-form solution for a European option's theoretical price. At the same time, the model generates

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option – an option whose payoff is determined by the average underlying price over some preset time period.

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Moran, Matthew. "Risk-adjusted Performance for Derivatives-based Indexes – Tools to Help Stabilize Returns".

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can be modeled as well as European ones. Binomial models are widely used by professional option traders. The

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borrowers have long had the option to repay the loan early, which corresponds to a callable bond option.

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A financial option is a contract between two counterparties with the terms of the option specified in a

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Contracts similar to options have been used since ancient times. The first reputed option buyer was the

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Today, many options are created in a standardized form and traded through clearing houses on regulated

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operates electronic and open outcry trading platforms. Eurex Exchange is owned by Eurex Frankfurt AG.

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The following are some principal valuation techniques used in practice to evaluate option contracts.

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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,

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are unit changes in the underlying's price, the underlying's volatility and time, respectively.

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option – any of a broad category of options that may include complex financial structures.

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option – an option that may be exercised only on specified dates on or before expiration.

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giving the right – but not the obligation – to dramatize a specific book or script.

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The most common way to trade options is via standardized options contracts listed by various

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Black, Fischer; Scholes, Myron (1973). "The Pricing of Options and Corporate Liabilities".

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The cost of holding a position in the underlying security, including interest and dividends

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Black, Fischer and Myron S. Scholes. "The Pricing of Options and Corporate Liabilities",

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Fischer Black and Myron S. Scholes. "The Pricing of Options and Corporate Liabilities",

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Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets

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In its most basic terms, the value of an option is commonly decomposed into two parts:

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Physical delivery option requires actual delivery of the goods or stocks to take place.

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contract up at the agreed upon price. The strike price may be set by reference to the

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are the standard hedge parameters calculated from an option valuation model, such as

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and offers insights for financial theory. A benchmark index for the performance of a

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Traders, Guns & Money: Knowns and unknowns in the dazzling world of derivatives

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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

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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:

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Maintenance of orderly markets, especially during fast trading conditions.

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Option Volatility and Pricing: Advanced Trading Strategies and Techniques

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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"

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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

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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

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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.

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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: 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:. 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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:. 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