Option

In finance, an option is a derivative financial instrument that specifies a contract between two parties for a future transaction on an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the corresponding obligation to fulfill the transaction. The price of an option derives from the difference between the reference price and the value of the underlying asset (commonly a stock, a bond, a currency or a futures contract) plus a premium based on the time remaining until the expiration of the option. Other types of options exist, and options can in principle be created for any type of valuable asset.

An option which conveys the right to buy something at a specific price is called a call; an option which conveys the right to sell something at a specific price is called a put. The reference price at which the underlying asset may be traded is called the strike price or exercise price. The process of activating an option and thereby trading the underlying at the agreed-upon price is referred to as exercising it. Most options have an expiration date. If the option is not exercised by the expiration date, it becomes void and worthless.

In return for assuming the obligation, called writing the option, the originator of the option collects a payment, the premium, from the buyer. The writer of an option must make good on delivering (or receiving) the underlying asset or its cash equivalent, if the option is exercised.

An option can usually be sold by its original buyer to another party. Many options are created in standardized form and traded on an anonymous options exchange among the general public, while other over-the-counter options are customized ad hoc to the desires of the buyer, usually by an investment bank.

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

Types

The Options can be classified into following types:

Exchange-traded options

Option styles

Naming 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 expiry.
  • 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 – any option that is not exotic.

Valuation models

The 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 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, 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–Scholes

Following early work by Louis Bachelier and later work by Edward O. ThorpFischer 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 theSwedish Central Bank‘s associated Prize for Achievement in Economics (a.k.a., the Nobel Prize in Economics), 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 model

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 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.

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