Deriscope ## The Excel Derivatives Periscope

##### Coverage

Variance_Swap

*Variance Swap* is a child type of Swap that represents an agreement to exchange once at swap's maturity the realized annualized "variance"*V* of the daily price returns of some underlying against a predetermined fixed amount.

The word "variance" is enclosed in double quotes to signify that *V* is computed in a slightly different way than from what implied by the regular statistical definition of variance.

More precisely, the mean of the daily price returns is ignored, so that *V* is defined as follows:

*V = (A/n)∑ᵢ(Rᵢ²)*

where

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

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

*Rᵢ* is the natural logarithmic return defined as

*Ri = ln(Pᵢ/Pᵢ₋₁)*

where

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

It turns out the payoff at maturity to the long holder of the swap equals *N(V-K)* where *Ν* is the so called "variance notional" and *K* is the strike.

The pricing methodology is specified in Model[Variance Swap]