Variance Swap is a of with functions , keys and example object 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)
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)
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