Variance Swap - Structure and Features

Structure and Features

The features of a variance swap include:

• the variance strike
• the realized variance
• the vega notional: Like other swaps, the payoff is determined based on a notional amount that is never exchanged. However, in the case of a variance swap, the notional amount is specified in terms of vega, to convert the payoff into dollar terms.

The payoff of a variance swap is given as follows:

where:

• = variance notional (a.k.a. variance units),
• = annualised realised variance, and
• = variance strike.

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 Define, for i=1 to n, the natural log returns. Then

where is an annualisation factor normally chosen to be approximately the number of sampling points in a year (commonly 252). It can be seen that subtracting the mean return will decrease the realised variance. If this is done, it is common to use as the divisor rather than, corresponding to an unbiased estimate of the sample variance.

It is market practice to determine the number of contract units as follows:

where is the corresponding vega notional for a volatility swap. This makes the payoff of a variance swap comparable to that of a volatility swap, another less popular instrument used to trade volatility.