Greeks

Explained:

Greeks


 
   

The Greeks are a set of factor sensitivities used extensively by traders to quantify the exposures of portfolios that contain options. Each measures how the portfolio's market value should respond to a change in some variable—an underlier, implied volatility, interest rate or time. There are five Greeks:

delta measures first order (linear) sensitivity to an underlier;

gamma measures second order (quadratic) sensitivity to an underlier;

vega measures first order (linear) sensitivity to the implied volatility of an underlier;

theta measures first order (linear) sensitivity to the passage of time;

rho measures first order (linear) sensitivity to an applicable interest rate.

They are called the Greeks because four out of the five are named after letters of the Greek alphabet. Vega is the exception. For reasons unknown, it is named after the brightest star in the constellation Lyra. At times, vega has been called kappa, but the name vega is now well established.

Four of the five are risk metrics. Theta is not because the passage of time in certain—it entails no risk. Theta is akin to the accrual of interest on a bond.

The Greeks are defined as first—and in the case of gamma, second—partial derivatives. See articles on each (linked above) for more information.

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delta and gamma Factor sensitivities measuring a portfolio's first and second order (linear and quadratic) sensitivity to the value of an underlier.

derivative instrument An instrument which derives its value from the value of other financial instruments. Article includes a list of vanilla and exotic derivatives.

financial risk management Practices by which a firm optimizes the manner in which it takes financial risk.

market risk Exposure to the uncertain market value of a portfolio.

option pricing theory The body of financial theory used by financial engineers to value options and other derivative instruments.

option spreads Positions combining one or more options in a single underlier.

put-call parity A formula that relates the price of a put to the price of a corresponding call.

rho Factor sensitivity measuring a portfolio's first order (linear) sensitivity to the risk-free rate.

scenario analysis Formalized "what if" analysis typically performed as a part of asset-liability management or corporate risk management.

theta Factor sensitivity measuring a portfolio's first order (linear) sensitivity to the passage of time.

value-at-risk A category of market risk measures.

vega Factor sensitivity measuring a portfolio's first order (linear) sensitivity to the implied volatility of an underlier.

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Greeks - Basics 18 Jul 2006
An insightful look at interdependencies between the Greeks.

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copyright © Glyn A. Holton, 1996

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