Correlation swap
title: "Correlation swap" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["derivatives-(finance)", "mathematical-finance", "banking", "swaps-(finance)"] topic_path: "economics" source: "https://en.wikipedia.org/wiki/Correlation_swap" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0
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_{\text{corr}} times the agreed strike \rho_{\text{strike}}, while the floating leg pays the realized correlation \rho_{\text{realized }}. The contract value at expiration from the pay-fixed perspective is therefore :N_{\text{corr}} (\rho_{\text{realized}}-\rho_{\text{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_{\text{realized }} := \frac{\sum_{i\neq j}{w_i w_j \rho_{i,j}}}{\sum_{i\neq j}{w_i w_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_{\text{realized }} = \frac{2}{n(n-1)}\sum_{i j}{\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.
Sources
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