Correlation swap

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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 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}}

Pricing and valuation[edit]

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

See also[edit]

Correlation of Nifty and VIX