Definition and application
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 the spot 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 a call, while one that conveys the right to sell at a specified price is known as a put. 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. The holder of an option may on-sell the option to a third party in a secondary market, in either anHistory
Historical uses of options
Contracts similar to options have been used since ancient times. The first reputed option buyer was theModern stock options
Options contracts have been known for decades. The Chicago 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 has increased since then. Today, many options are created in a standardized form and traded through clearing houses on regulated options exchanges, while otherContract specifications
A financial option is a contract between two counterparties with the terms of the option specified in a term sheet. Option contracts may be quite complicated; however, at minimum, they usually contain the following specifications: * whether the option holder has the right to buy (a call option) or the right to sell (a put option) * the quantity and class of the underlying asset(s) (e.g., 100 shares of XYZ Co. B stock) * the strike price, also known as the exercise price, which is the price at which the underlying transaction will occur upon exercise * the expiration date, or expiry, which is the last date the option can be exercised * the settlement 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 writerOption trading
Forms of trading
Exchange-traded options
Exchange-traded options (also called "listed options") are a class of exchange-traded derivatives. Exchange-traded options have standardized contracts, and are settled through aOver-the-counter options
Exchange trading
The most common way to trade options is via standardized options contracts that are listed by various futures and options exchanges. Listings and prices are tracked and can be looked up by ticker symbol. By publishing continuous, live markets for option prices, an exchange enables independent parties to engage in price 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 highestBasic trades (American style)
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 hedging. An option contract in US markets usually represents 100 shares of the underlying security.Long call
A trader who expects a stock's price to increase can buy a call 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 premium paid is 10, then if the spot price of 100 rises to only 110 the transaction is break-even; an increase in 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).Long put
A trader who expects a stock's price to decrease can buy a put option to sell the stock at a fixed price (strike price) at a later date. The trader is under no obligation 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 be shorted.Short call
A trader who expects a stock's price to decrease can sell the stock short 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.Short put
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 the CBOE S&P 500 PutWrite Index (ticker PUT).Options strategies
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 options 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 a butterfly 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. A condor is a strategy that is 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 a straddle (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 the strangle 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 the covered call, in which a trader buys a stock (or holds a previously-purchased long stock position), and sells a call. (This can be contrasted with a naked call. See also naked 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 as put–call parity and offers insights for financial theory. A benchmark index for the performance of a buy-write strategy is the CBOE S&P 500 BuyWrite Index (ticker symbol BXM). Another very common strategy is the protective 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 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.Types
Options can be classified in a few ways.According to the option rights
* Call options give the holder the right – but not the obligation – to buy something at a specific price for a specific time period. * Put options give the holder the right – but not the obligation – to sell something at a specific price for a specific time period.According to the underlying assets
* Equity option * Bond option * Future option * Index option * Commodity option * Currency option * Swap optionOther option types
Another important class of options, particularly in the U.S., areOption styles
Options are classified into a number of styles, the most common of which are: * American option – an option that may be exercised on any trading day on or before expiration. * European option – an option that may only be exercised on expiry. These are often described as vanilla 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. *Valuation
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 rational pricing (i.e. risk neutrality), moneyness, option time value, and put–call parity. The valuation itself combines a model of the behavior ( "process") 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) Black–Scholes model for equities, to the Heath–Jarrow–Morton framework for interest rates, to the Heston model where volatility itself is considered stochastic. See Asset pricing for a listing of the various models here.Basic decomposition
In its most basic terms, the value of an option is commonly decomposed into two parts: * The first part is the intrinsic value, which is defined as the difference between the market value of the underlying, and the strike price of the given option * The second part is the time value, which depends on a set of other factors which, through a multi-variable, non-linear interrelationship, reflect the discounted expected value of that difference at expiration.Valuation models
As above, the value of the option is estimated using a variety of quantitative techniques, all based on the principle of risk-neutral pricing, and using stochastic calculus in their solution. The most basic model is the Black–Scholes model. More sophisticated models are used to model the volatility smile. These models are implemented using a variety of numerical techniques. In general, standard option valuation models depend on the following factors: * The current market price of the underlying security * The strike 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 to expiration together with any restrictions on when exercise may occur * an estimate of the future volatility 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 of the principal valuation techniques used in practice to evaluate option contracts.Black–Scholes
Following early work by Louis Bachelier and later work by Robert C. Merton, Fischer Black and Myron 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. At the same time, the model generates hedge 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 the Swedish Central Bank's associated Prize for Achievement in Economics (a.k.a., theStochastic volatility models
Since the market crash of 1987, it has been observed that market implied volatility for options of lower strike prices are 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 volatility smile; and with a time dimension, a volatility surface. The main approach here is to treat volatility as stochastic, with the resultant stochastic volatility models, and the Heston model as prototype; see #Risk-neutral_measure for a discussion of the logic. Other models include the CEV and SABR volatility models. One principal advantage of the Heston model, however, is that it can be solved in closed-form, while other stochastic volatility models require complex numerical methods. An alternate, though related, approach is to apply a local volatility model, where volatility is treated as a '' deterministic'' function of both the current asset level and of time . As such, a local volatility model is a generalisation of the Black–Scholes model, where the volatility is a constant. The concept was developed when Bruno Dupire and Emanuel Derman and Iraj Kani 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.Short-rate models
For the valuation of bond options, swaptions (i.e. options on swaps), and interest rate cap and floors (effectively options on the interest rate) various short-rate models have been developed (applicable, in fact, to interest rate derivatives generally). The best known of these are Black-Derman-Toy and Hull–White. These models describe the future evolution of interest rates by describing the future evolution of the short rate. The other major framework for interest rate modelling is the Heath–Jarrow–Morton framework (HJM). The distinction is that HJM gives an analytical description of the ''entire'' yield curve, rather than just the short rate. (The HJM framework incorporates theModel implementation
Once a valuation model has been chosen, there are a number of different techniques used to implement the models.Analytic techniques
In some cases, one can take the mathematical model and using analytical methods, develop closed form solutions such as the Black–Scholes model and the Black model. The resulting solutions are readily computable, as are their "Greeks". Although the Roll–Geske–Whaley model applies to an American call with one dividend, for other cases of American options, closed form solutions are not available; approximations here include Barone-Adesi and Whaley, Bjerksund and Stensland and others.Binomial tree pricing model
Closely following the derivation of Black and Scholes, John Cox, Stephen Ross and Mark Rubinstein developed the original version of the binomial options pricing model. It models the dynamics of the option's theoretical value for discrete 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, and American options can be modeled as well as European ones. Binomial models are widely used by professional option traders. The trinomial 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, see Lattice model (finance).Monte Carlo models
For many classes of options, traditional valuation techniques are intractable 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 simulation 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 expectation value for the option. Note though, that despite its flexibility, using simulation for American styled options is somewhat more complex than for lattice based models.Finite difference models
The equations used to model the option are often expressed as partial differential equations (see for exampleOther models
Other numerical implementations which have been used to value options include finite element methods.Risks
As with all securities, trading options entails the risk of the option's value changing over time. However, unlike traditional securities, thePin risk
A special situation called pin 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.Counterparty risk
A further, often ignored, risk in derivatives such as options isOptions approval levels
To limit risk, brokers use access 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 like naked calls and naked puts. Traders can update their information when requesting permission to upgrade to a higher approval level.See also
* American Stock Exchange * Area yield options contract * Ascot (finance) * Chicago Board Options Exchange * Dilutive security * Eurex * Euronext.liffe * International Securities Exchange * NYSE Arca * Philadelphia Stock Exchange * LEAPS (finance) * Options backdating * Options Clearing Corporation * Options spread * Options strategy * Option symbol * Real options analysis * PnL Explained * Pin risk (options) * XVAReferences
Further reading
* Fischer Black and Myron S. Scholes. "The Pricing of Options and Corporate Liabilities,"