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An option is a financial instrument that gives its holder the right, but not the obligation, to buy or sell something at a specified time in the future, the maturity of the option, for a pre-specified price, called the strike price. If the right to buy or sell is invoked then it is said that the option is exercised. Rational pricing of options is an important topic in economics, finance, and financial mathematics, and gained much momentum through the work of Fisher Black, Myron Scholes and Robert Merton who introduced the now famous Black-Scholes formula for option pricing (Merton independently derived the Black and Scholes using a different method, with the advantage of allowing the formula to be generalized in several directions[1]). For their work on rational pricing of options Scholes and Merton were honored with the 1997 Nobel Prize in Economics (Fisher Black would have shared this honor as well, but he passed away in 1995).

Call and put options

Depending on whether an option gives the right to buy or sell assets, two different types of options can be identified. An option that gives the buyer the right to buy assets at the strike price is called a call option, while an option that gives the right to sell assets is called a put option.

Why use an option

listed shares


unlisted shares

real estate property - arm-length - upon death


American vs. European options

Depending on whether an option allows one to exercise it before and at maturity, or only at maturity, one can differentiate at least two different types of options:

A European option allows its holder to exercise the option only at maturity.

An American option allows the holder to exercise the option at any time before and including the maturity.

In rational pricing, an American option should be worth more than a European option because it gives a holder of the former the same right as a holder of the latter and more. However, if there the risk-free interest rate is non-negative then American and European options of the same strike price and maturity on a non-dividend paying stock are worth the same.

who sells options



anyone else

Guarantees an option will be fulfilled.

Option costs

For listed securities: Black . . . model



  1. 1997 Nobel Prize in Economics Press Release, http://nobelprize.org/nobel_prizes/economics/laureates/1997/press.html, The Royal Swedish Academy of Sciences, 14 October 1997 (retrieved 2007-07-7).