In finance, an option is a contract between a buyer and a seller that gives the buyer of the option the right, but not the obligation, to buy or to sell a specified asset (underlying) on or before the option's expiration time, at an agreed price, the strike price.
In return for granting the option, the seller collects a payment (the premium ) from the buyer. Granting the option is also refered to as "selling" or "writing" the option.
- A call option gives the buyer of the option the right to buy the underlying at the strike price.
- A put option gives the buyer of the option the right to sell the underlying at the strike price.
If the buyer chooses to exercise this right, the seller is obliged to sell or buy the asset at the agreed price. The buyer may choose not to exercise the right and let it expire. The underlying asset can be a piece of property, a security (stock or bond), or a derivative instrument, such as a futures contract.
The theoretical value of an option is evaluated according to several models. These models, which are developed by quantitative analysts, attempt to predict how the value of an option changes in response to changing conditions. Hence, the risks associated with granting, owning, or trading options may be quantified and managed with a greater degree of precision, perhaps, than with some other investments. Exchange-traded options form an important class of options which have standardized contract features and trade on public exchanges, facilitating trading among independent parties. Over-the-counter options are traded between private parties, often well-capitalized institutions that have negotiated separate trading and clearing arrangements with each other.
Another important class of options, particularly in the U.S., are employee stock options, which are awarded by a company to their employees as a form of incentive compensation. Other types of options exist in many financial contracts, for example real estate options are often used to assemble large parcels of land, and prepayment options are usually included in mortgage loans. However, many of the valuation and risk management principles apply across all financial options.
Contract specifications
Every financial option is a contract between the 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 writer of the option.
Types of options
The primary types of financial options are:
- Exchange traded options (also called "listed options") are a class of exchange traded derivatives. Exchange traded options have standardized contracts, and are settled through a clearing house with fulfillment guaranteed by the credit of the exchange. Since the contracts are standardized, accurate pricing models are often available. Exchange traded options include:
- stock options,
- commodity options,
- bond options and other interest rate options
- stock market index options or, simply, index options and
- options on futures contracts
- 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, at least one of the counterparties to an OTC option is a well-capitalized institution. Option types commonly traded over the counter include:
- interest rate options
- currency cross rate options, and
- options on swaps or swaptions.
- Employee stock options are issued by a company to its employees as compensation.
Option styles
Main article: Option styleNaming conventions are used to help identify properties common to many different types of options. These include:
- European option - an option that may only be exercised on expiration.
- American option - an option that may be exercised on any trading day on or before expiration.
- Bermudan option - an option that may be exercised only on specified dates on or before expiration.
- 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
- Exotic option - any of a broad category of options that may include complex financial structures.
- Vanilla option - by definition, any option that is not exotic.
Valuation models
Main article: Valuation of optionsThe value of an option can be estimated using a variety of quantitative techniques based on the concept of risk neutral pricing and using stochastic calculus. 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 underlier (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, and
- 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
Main article: Black–ScholesIn the early 1970s, 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 (often mistakenly referred to as the Nobel Prize), the application of the model in actual options trading is clumsy because of the assumptions of continuous (or no) dividend payment, 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.
Stochastic volatility models
Main article: Heston modelSince 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 is stochastic, varying both for time and for the price level of the underlying security. Stochastic volatility models have been developed including one developed by S.L. Heston. One principal advantage of the Heston model is that it can be solved in closed-form, while other stochastic volatility models require complex numerical methods.
Model implementation
Further information: Valuation of optionsOnce a valuation model has been chosen, there are a number of different techniques used to take the mathematical models 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 Black-Scholes and the Black model. The resulting solutions are useful because they are rapid to calculate.
Binomial tree pricing model
Main article: Binomial options pricing modelClosely 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 duration. The model starts with a binomial tree of discrete future possible underlying stock prices. By
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