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 .

One leg of the swap will pay an amount based upon the realized variance of the price changes of the underlying product. Conventionally, these price changes will be daily log returns, based upon the most commonly used closing price. The other leg of the swap will pay a fixed amount, which is the strike, quoted at the deal's inception. Thus the net payoff to the counterparties will be the difference between these two and will be settled in cash at the expiration of the deal, though some cash payments will likely be made along the way by one or the other counterparty to maintain agreed upon margin.

The features of a variance swap include:

The payoff of a variance swap is given as follows:

where:

The annualised realised variance is calculated based on a prespecified set of sampling points over the period. It does not always coincide with the classic statistical definition of variance as the contract terms may not subtract the mean. For example, suppose that there are n+1 sample points ${\displaystyle S_{\text{0}},S_{\text{1}},...,S_{\text{n}}.}$ Define, for i=1 to n, ${\displaystyle R_{\text{i}}=\ln(S_{\text{i}}/S_{\text{i-1}}),}$ the natural log returns. Then

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