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 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 w_i on n securities, the realized correlation is defined as the weighted average of all pairwise correlation coefficients \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: 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.

Sources