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 formula_1 times the agreed strike formula_2, while the floating leg pays the realized correlation formula_3. The contract value at expiration from the pay-fixed perspective is therefore 
formula_4
Given a set of nonnegative weights formula_5 on formula_6 securities, the realized correlation is defined as the weighted average of all pairwise correlation coefficients formula_7:
formula_8
Typically formula_7 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:
formula_10
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.