Correlation

From WilmottWiki

Correlation is a measure of the level of co-dependence between two random variables. A correlation of +1 means that the two variables increase or decrease simultaneously, while a correlation of -1 means that the two variables move in opposite directions. A correlation of 0 may indicate that the two variables are independent.

In finance, correlation is almost always measured on returns rather than prices.

Definitions

Realised/historical correlation is the observed statistical co-dependence between the returns of two assets, over a given period of time. For example, the realised correlation of weekly returns between the S&P 500 and DowJones EuroStoxx 50 indices from 30 November 2005 until 30 November 2006 was 79%.

Implied correlation is the number you have to put into the generalised Black-Scholes option pricing equation for two assets to get the theoretical price to match the market price. Often said to be the market's estimate of future realised correlation. Because options on several underlyings are almost always traded over-the-counter, implied correlation is not publicly observable, with the exception of the average correlation between the constituents of liquid equity indices.