Infinance, anoption is a contract which conveys to its owner, theholder, the right, but not the obligation, to buy or sell a specific quantity of anunderlyingasset orinstrument at a specifiedstrike price on or before a specifieddate, depending on thestyle of the option.
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 (or contingent liability) and have avaluation that may depend on a complex relationship between underlying asset price, time until expiration,market volatility, the risk-free rate of interest, and the strike price of the option.
Options may be traded between private parties inover-the-counter (OTC) transactions, or they may be exchange-traded in live, public markets in the form of standardized contracts.
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 contract up at the agreed upon price. The strike price may be set by reference to thespot price (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 acall, while one that conveys the right to sell at a specified price is known as aput.
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 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.
An option holder may on-sell the option to a third party in asecondary market, in either anover-the-counter transaction or on anoptions exchange, 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 adividend.
Contracts similar to options have been used since ancient times.[1] The first reputed option buyer was theancient Greek mathematician and philosopherThales of Miletus. On a certain occasion, it was predicted that the season'solive 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 his 'option'.[2][3]
The 1688 bookConfusion of Confusions describes the trading of "opsies" on the Amsterdam stock exchange (nowEuronext), explaining that "there will be only limited risks to you, while the gain may surpass all your imaginings and hopes."[4]
In London, puts and "refusals" (calls) first became well-known trading instruments in the 1690s during the reign ofWilliam andMary.[5] 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.
In thereal estate 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 real property, like houses, requires a buyer paying the seller into anescrow account anearnest payment, which offers the buyer the right to buy the property at the set terms, including the purchase price.[citation needed]
Lines of credit give the potential borrower the right – but not the obligation – to borrow within a specified time period.
Many choices, or embedded options, have traditionally been included inbond contracts. For example, many bonds areconvertible into common stock at the buyer's option, or may be called (bought back) at specified prices at the issuer's option.Mortgage borrowers have long had the option to repay the loan early, which corresponds to a callable bond option.
Options contracts have been known for decades. TheChicago Board Options Exchange 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.
Today, many options are created in a standardized form and traded through clearing houses on regulatedoptions exchanges. In contrast, otherover-the-counter 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 asderivative products, or simply, derivatives.[6][7]
A financial option is a contract between two counterparties with the terms of the option specified in aterm sheet. Option contracts may be quite complicated; however, at minimum, they usually contain the following specifications:[8]
whether the option holder has the right to buy (acall option) or the right to sell (aput option)
the quantity and class of theunderlying asset(s) (e.g., 100 shares of XYZ Co. B stock)
thestrike price, also known as the exercise price, which is the price at which the underlying transaction will occur uponexercise
theexpiration date, or expiry, which is the last date the option can be exercised
thesettlement terms, for instance, whether the writer must deliver the actual asset on exercise, or may simply tender the equivalent cash amount
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
Exchange-traded options (also called "listed options") are a class ofexchange-traded derivatives. Exchange-traded options have standardized contracts and are settled through aclearing house with fulfillment guaranteed by theOptions Clearing Corporation (OCC). Since the contracts are standardized, accurate pricing models are often available. Exchange-traded options include:[9][10]
Over-the-counter 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 prevent credit risk). Option types commonly traded over the counter include:
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 counterparties must establish credit lines with each other and conform to each other's clearing and settlement procedures.
The most common way to trade options is via standardized options contracts listed by variousfutures and options exchanges.[12] Listings and prices are tracked and can be looked up byticker symbol. By publishing continuous, live markets for option prices, an exchange enables independent parties to engage inprice discovery and execute transactions. As an intermediary to both sides of the transaction, the benefits the exchange provides to the transaction include:
Fulfillment of the contract is backed by the credit of the exchange, which typically has the highestrating (AAA),
Counterparties remain anonymous,
Enforcement of market regulation to ensure fairness and transparency, and
Maintenance of orderly markets, especially during fast trading conditions.
Days till Expiration vs Option Volume (7000+ contracts)
These trades are described from the point of view of a speculator. If they are combined with other positions, they can also be used inhedging. An option contract in US markets usually represents 100 shares of the underlying security.[13][14]
A trader who expects a stock's price to increase can buy acall option to purchase the stock at a fixed price (strike price) 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.
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 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.
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).
A trader who expects a stock's price to decrease can buy aput option 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 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.
The trader exercising a put option on a stock does not need to own the underlying asset, because most stocks can beshorted.
A trader who expects a stock's price to decrease can sell the stockshort 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 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.
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 (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 theCBOE S&P 500 PutWrite Index (ticker PUT).
Payoffs from buying a butterfly spreadPayoffs from selling a straddlePayoffs from a covered call
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 ofoptions strategies. Simple strategies usually combine only a few trades, while more complicated strategies can combine several.
Strategies are often used to engineer a particular risk profile to movements in the underlying security. For example, buying abutterfly 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.
Acondor 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.
Selling astraddle (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.
Similar to the straddle is thestrangle 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.
One well-known strategy is thecovered call, in which a trader buys a stock (or holds a previously purchased stock position), and sells a call. (This can be contrasted with anaked call. See alsonaked put.) 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 asput–call parity and offers insights for financial theory. A benchmark index for the performance of abuy-write strategy is theCBOE S&P 500 BuyWrite Index (ticker symbol BXM).
Another very common strategy is theprotective put, 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.
Another important class of options, particularly in the U.S., areemployee stock options, which a company awards to their employees as a form of incentive compensation. Other types of options exist in many financial contracts. For examplereal estate options are often used to assemble large parcels of land, andprepayment options are usually included inmortgage loans. However, many of the valuation and risk management principles apply across all financial options.
Options are classified into a number of styles, the most common of which are:
American option – an option that may beexercised on any trading day on or beforeexpiration.
European option – an option that may only be exercised on expiry.
These are often described asvanilla options. Other styles include:
Bermudan option – an option that may be exercised only on specified dates on or before expiration.
Asian option – an option whose payoff is determined by the average underlying price over some preset time period.
Barrier 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.
Binary option – An all-or-nothing option that pays the full amount if the underlying security meets the defined condition on expiration, otherwise, it expires.
Exotic option – any of a broad category of options that may include complex financial structures.[15]
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 ofrational pricing (i.e.risk neutrality),moneyness,option time value, andput–call parity.
In its most basic terms, the value of an option is commonly decomposed into two parts:
The first part is theintrinsic value, which is defined as the difference between the market value of theunderlying, and the strike price of the given option
The second part is thetime value, which depends on a set of other factors which, through a multi-variable, non-linear interrelationship, reflect thediscountedexpected value of that difference at expiration.
As above, the value of the option is estimated using a variety of quantitative techniques, all based on the principle ofrisk-neutral pricing and usingstochastic calculus in their solution. The most basic model is theBlack–Scholes model. More sophisticated models are used to model thevolatility smile. These models are implemented using a variety of numerical techniques.[18] In general, standard option valuation models depend on the following factors:
The current market price of the underlying security
Thestrike price of the option, particularly in relation to the current market price of the underlying (in the money vs. out of the money)
The cost of holding a position in the underlying security, including interest and dividends
The time toexpiration together with any restrictions on when exercise may occur
an estimate of the futurevolatility of the underlying security's price over the life of the option
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.
The following are some principal valuation techniques used in practice to evaluate option contracts.
Following early work byLouis Bachelier and later work byRobert C. Merton,Fischer Black andMyron Scholes 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 produced a closed-form solution for a European option's theoretical price.[19] At the same time, the model generateshedge parameters necessary for effective risk management of option holdings.
While the ideas behind the Black–Scholes model were ground-breaking and eventually led to Scholes and Merton receiving theSwedish Central Bank's associatedPrize for Achievement in Economics (a.k.a., theNobel Prize in Economics),[20] 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 financial market in which the result is within the reasonable range.[21]
Since themarket crash of 1987, it has been observed that marketimplied volatility 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-calledvolatility smile; and with a time dimension, avolatility surface.
An alternate, though related, approach is to apply alocal volatility model, wherevolatility is treated as adeterministic function of both the current asset level and of time. As such, a local volatility model is a generalisation of theBlack–Scholes model, where the volatility is a constant. The concept was developed whenBruno Dupire[23] andEmanuel Derman andIraj Kani[24] noted that there is a unique diffusion process consistent with the risk neutral densities derived from the market prices of European options. See#Development for discussion.
For the valuation ofbond options,swaptions (i.e. options onswaps), andinterest rate cap and floors (effectively options on the interest rate) variousshort-rate models have been developed (applicable, in fact, tointerest rate derivatives generally). The best known of these areBlack-Derman-Toy andHull–White.[25] These models describe the future evolution ofinterest rates by describing the future evolution of the short rate. The other major framework for interest rate modelling is theHeath–Jarrow–Morton framework (HJM). The distinction is that HJM gives an analytical description of theentireyield curve, rather than just the short rate. (The HJM framework incorporates theBrace–Gatarek–Musiela model andmarket models. And some of the short rate models can be straightforwardly expressed in the HJM framework.) For some purposes, e.g., valuation ofmortgage-backed securities, 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, theBlack model can instead be employed, with certain assumptions.
Closely following the derivation of Black and Scholes,John Cox,Stephen Ross andMark Rubinstein developed the original version of thebinomial options pricing model.[26][27] It models the dynamics of the option's theoretical value fordiscrete time 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 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, andAmerican options can be modeled as well as European ones. Binomial models are widely used by professional option traders. Thetrinomial tree 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 and hybrid instruments, seeLattice model (finance).
For many classes of options, traditional valuation techniques areintractable 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 usessimulation 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 anexpectation value for the option.[28] Note though, that despite its flexibility, using simulation forAmerican styled options is somewhat more complex than for lattice based models.
The equations used to model the option are often expressed aspartial differential equations (see for exampleBlack–Scholes equation). Once expressed in this form, afinite difference model can be derived, and the valuation obtained. A number of implementations of finite difference methods exist for option valuation, including:explicit finite difference,implicit finite difference and theCrank–Nicolson method. 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 nottractable in closed form.
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,,, 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:
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).
As with all securities, trading options entails the risk of the option's value changing over time. However, unlike traditional securities, thereturn 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.
In general, the change in the value of an option can be derived fromItô's lemma as:
where theGreeks,, and are the standard hedge parameters calculated from an option valuation model, such asBlack–Scholes, and, and are unit changes in the underlying's price, the underlying's volatility and time, respectively.
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,, and, 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 of shares in the underlying, a trader can form adelta neutral portfolio that is hedged from loss for small changes in the underlying's price. The corresponding price sensitivity formula for this portfolio is:
A special situation calledpin risk 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 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.
A further, often ignored, risk in derivatives such as options iscounterparty risk. 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.
To limit risk, brokers useaccess control 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 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 likenaked calls andnaked puts. Traders can update their information when requesting permission to upgrade to a higher approval level.[29]
The Chicago Board Options Exchange (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 theS&P 500 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-electronic trading platform. The CBOE is regulated by theU.S. Securities and Exchange Commission (SEC).[30]
Founded in 1790, TheNASDAQ OMX PHLX, also known as thePhiladelphia Stock Exchange 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 the U.S. In 2008,NASDAQ acquired the Philadelphia Stock Exchange and renamed it NASDAQ OMX PHLX. It operates as a subsidiary of NASDAQ, Inc.[31]
International Securities Exchange (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.[32]
Eurex Exchange 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 operates electronic and open outcry trading platforms. Eurex Exchange is owned by Eurex Frankfurt AG.[33]
Founded in 1878, theTokyo Stock Exchange (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 theFinancial Services Agency of Japan. It is owned by theJapan Exchange Group.[34]
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