# Correlation swap

A **correlation swap** is an over-the-counter financial derivative that allows one to speculate on or hedge risks associated with the observed average correlation, of a collection of underlying products, where each product has periodically observable prices, as with a commodity, exchange rate, interest rate, or stock index.

## Payoff Definition[edit]

The fixed leg of a correlation swap pays the notional times the agreed strike , while the floating leg pays the realized correlation . The contract value at expiration from the pay-fixed perspective is therefore

Given a set of nonnegative weights on securities, the realized correlation is defined as the weighted average of all pairwise correlation coefficients :

Typically would be calculated as the Pearson correlation coefficient between the daily log-returns of assets *i* and *j*, possibly under zero-mean assumption.

Most correlation swaps trade using equal weights, in which case the realized correlation formula simplifies to:

The specificity of correlation swaps is somewhat counterintuitive, as the protection buyer pays the fixed, unlike in usual swaps.

## Pricing and valuation[edit]

No industry-standard models yet exist that have stochastic correlation and are arbitrage-free.

## See also[edit]

## Sources[edit]

- Meissner, Gunter (2014).
*Correlation risk modeling and management : an applied guide including the Basel III correlation framework-- with interactive models in Excel/VBA*. Wiley. p. 11. ISBN 111879690X.