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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

The fixed leg of a correlation swap pays the notional Ncorr times the agreed strike ρstrike, while the floating leg pays the realized correlation ρrealized . The contract value at expiration from the pay-fixed perspective is therefore

Ncorr(ρrealizedρstrike)

Given a set of nonnegative weights wi on n securities, the realized correlation is defined as the weighted average of all pairwise correlation coefficients ρi,j:

ρrealized :=ijwiwjρi,jijwiwj

Typically ρi,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:

ρrealized =2n(n1)i<jρi,j

Pricing and valuation

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

See also

References

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