Trisha Shetty (Editor)

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.

Contents

Payoff Definition

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

N corr ( ρ realized − ρ 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 ρ i , j :

ρ realized  := ∑ i ≠ j w i w j ρ i , j ∑ i ≠ j w i w j

Typically ρ 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:

ρ realized  = 2 n ( n − 1 ) ∑ i > j ρ i , j

Pricing and valuation

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

References

Correlation swap Wikipedia
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