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A correlation swap is an
over-the-counter Over-the-counter (OTC) drugs are medicines sold directly to a consumer without a requirement for a prescription from a healthcare professional, as opposed to prescription drugs, which may be supplied only to consumers possessing a valid prescr ...
financial derivative In finance, a derivative is a contract that ''derives'' its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and is often simply called the "underlying". Derivatives can be u ...
that allows one to
speculate In finance, speculation is the purchase of an asset (a commodity, goods, or real estate) with the hope that it will become more valuable shortly. (It can also refer to short sales in which the speculator hopes for a decline in value.) Many s ...
on or
hedge A hedge or hedgerow is a line of closely spaced shrubs and sometimes trees, planted and trained to form a barrier or to mark the boundary of an area, such as between neighbouring properties. Hedges that are used to separate a road from adjoini ...
risks In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environme ...
associated with the observed average
correlation In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics ...
, of a collection of
underlying In finance, a derivative is a contract that ''derives'' its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and is often simply called the "underlying". Derivatives can be use ...
products, where each product has periodically observable prices, as with a
commodity In economics, a commodity is an economic good, usually a resource, that has full or substantial fungibility: that is, the market treats instances of the good as equivalent or nearly so with no regard to who produced them. The price of a comm ...
,
exchange rate In finance, an exchange rate is the rate at which one currency will be exchanged for another currency. Currencies are most commonly national currencies, but may be sub-national as in the case of Hong Kong or supra-national as in the case of ...
,
interest rate An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, th ...
, or
stock index In finance, a stock index, or stock market index, is an index that measures a stock market, or a subset of the stock market, that helps investors compare current stock price levels with past prices to calculate market performance. Two of the pri ...
.


Payoff Definition

The fixed leg of a correlation swap pays the notional N_ times the agreed strike \rho_, while the floating leg pays the realized correlation \rho_. The contract value at expiration from the pay-fixed perspective is therefore :N_ (\rho_-\rho_) 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_: :\rho_ := \frac Typically \rho_ would be calculated as the
Pearson correlation coefficient In statistics, the Pearson correlation coefficient (PCC, pronounced ) ― also known as Pearson's ''r'', the Pearson product-moment correlation coefficient (PPMCC), the bivariate correlation, or colloquially simply as the 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_ = \frac\sum_ 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 In economics and finance, arbitrage (, ) is the practice of taking advantage of a difference in prices in two or more markets; striking a combination of matching deals to capitalise on the difference, the profit being the difference between the ...
-free.


See also

*
Variance swap A variance swap is an over-the-counter financial derivative that allows one to speculate on or hedge risks associated with the magnitude of movement, i.e. volatility, of some underlying product, like an exchange rate, interest rate, or stock index. ...
*
Rainbow option Rainbow option is a derivative exposed to two or more sources of uncertainty, as opposed to a simple option that is exposed to one source of uncertainty, such as the price of underlying asset. The name of ''rainbow'' comes from Rubinstein (1991), ...


Sources

* {{Derivatives market Derivatives (finance) Mathematical finance Banking Swaps (finance)