# Variance Swap

According to the concept of finance, the variance swap is referred as the financial derivative, the payoff of which is equal to the annualized realized variance of returns on the fixed quantity and underlying price.

The annualized realized variance here is defined as the difference that is there between the squares of annualized realized volatility.

The variance swap features include – the realized variance, the variance strike and the vega notional. For the vega notional, the payoff is calculated on the basis of the notional amount, which is never exchanged. But the notional amount of variance swap is specified in terms of vega in order to convert the payoff into dollar terms.

The following formula gives the mathematical interpretation of the payoff of a variance swap:

Nvar = (σ2realized ? σ2strike)

Here,

Nvar refers to variance notional

σ2realized realized refers to the annualized realized variance

σ2strike strike refers to the variance strike

The annualized realized variance is determined on the basis of the pre-specified set of sampling points spread over the period. It follows the general market convention of not subtracting the mean and does not concur with the variances classic statistical definition.

According to the market practice, the number of contract units is determined by the following formula:

Nvar = Nvol / 2 σstrike

Here, Nvol refers to the corresponding volatility swap vega notional

This mathematical formula allows the payoff of a variance swap to be comparable with that of the volatility swap. This instrument is less popularly used to trade the volatility. Variance swaps are useful in trading the volatility directly. Options strategies are also used to trade volatility. But the strategies, which are not delta neutral, can cause vulnerability with the underlying price movements. In those cases when the investors use delta neutral options strategy, the profit and loss profile of the investors show a type of dependence on the underlying price and time that is complicated in nature. 