## Variance Swap

**is a direct subtype of Swap with functions Variance Swap Functions, keys Variance Swap keys and example object VarSwap that represents an agreement to exchange once at swap's maturity the realized annualized "variance"**

*Variance Swap***of the daily price returns of some underlying against a predetermined fixed amount.**

*V*The word "variance" is enclosed in double quotes to signify that

**is computed in a slightly different way than from what implied by the regular statistical definition of variance.**

*V*More precisely, the mean of the daily price returns is ignored, so that

**is defined as follows:**

*V*

*V = (A/n)∑ᵢ(Rᵢ²)*where

**is an annualization factor, typically equal to 252, required to transform the daily variance into annualized variance**

*A***is the number of sampling points, or equivalently the number of dates - except the first - where the underlying price is recorded**

*n***is the natural logarithmic return defined as**

*Rᵢ*

*Ri = ln(Pᵢ/Pᵢ₋₁)*where

**is the underlying price at the ith sampling date.**

*Pᵢ*It turns out the payoff at maturity to the long holder of the swap equals

**where**

*N(V-K)***is the so called "variance notional" and**

*Ν***is the strike.**

*K*The pricing methodology is specified in Model[Variance Swap]