A correlation swap is an over-the-counter

Over-the-counter (finance)

Within the derivatives markets, many products are traded through exchanges. An exchange has the benefit of facilitating liquidity and also mitigates all credit risk concerning the default of a member of the exchange. Products traded on the exchange must be well standardised to transparent trading....

 financial derivative that allows one to speculate on or hedge

Hedge (finance)

A hedge is an investment position intended to offset potential losses that may be incurred by a companion investment.A hedge can be constructed from many types of financial instruments, including stocks, exchange-traded funds, insurance, forward contracts, swaps, options, many types of...

 risks associated with the observed average correlation

Correlation

In statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence....

, of a collection of underlying

Underlying

In finance, the underlying of a derivative is an asset, basket of assets, index, or even another derivative, such that the cash flows of the derivative depend on the value of this underlying...

 products, where each product has periodically observable prices, as with a commodity

Commodity

In economics, a commodity is the generic term for any marketable item produced to satisfy wants or needs. Economic commodities comprise goods and services....

, exchange rate

Exchange rate

In finance, an exchange rate between two currencies is the rate at which one currency will be exchanged for another. It is also regarded as the value of one country’s currency in terms of another currency...

, interest rate

Interest rate

An interest rate is the rate at which interest is paid by a borrower for the use of money that they borrow from a lender. For example, a small company borrows capital from a bank to buy new assets for their business, and in return the lender receives interest at a predetermined interest rate for...

, or stock index.

Payoff Definition

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

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

Pricing and valuation

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

Arbitrage

In economics and finance, arbitrage is the practice of taking advantage of a price difference between two or more markets: striking a combination of matching deals that capitalize upon the imbalance, the profit being the difference between the market prices...

-free.