Correlation swap explained

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

The fixed leg of a correlation swap pays the notional

N _{corr} times the agreed strike \rho _{strike} , while the floating leg pays the realized correlation \rho _{realized} . The contract value at expiration from the pay-fixed perspective is therefore N _{corr} (\rho _{realized} - \rho _{strike} )

Given a set of nonnegative weights

w _{i} on n securities, the realized correlation is defined as the weighted average of all pairwise correlation coefficients \rho _{i,j} :\rho _{realized} : = (\sum _{i ≠} {w _{i} w _{j} \rho _{i,j})/() }Typically \rho _{i,j} 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:

\rho _{realized} = (2)/(n(n -1 )) \sum _{i} {\rho _{i,j} }

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

Pricing and valuation

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

See also

• Variance swap
• Rainbow option

Sources

• Book: Meissner . Gunter . Correlation risk modeling and management : an applied guide including the Basel III correlation framework-- with interactive models in Excel/VBA . 2014 . Wiley . 978-1118796900 . 11.