A variance swap is a financial derivative that allows one to speculate on or hedge risks associated with the magnitude of movement, i.e. volatility, of some underlying product, like an exchange rate, interest rate, or stock index.
A Variance Swap is a type of volatility swap where the payout is linear to variance rather than volatility. Therefore, the payout will rise at a higher rate than volatility. Variance is the square of standard deviation. Because of this, a variance swaps’ payout will be larger than that of a volatility swap, as these products are based upon variance rather than standard deviation.
One leg of the swap will pay an amount based upon the realized variance of the price changes of the underlying product. Conventionally, these price changes will be daily log returns, based upon the most commonly used closing price. The other leg of the swap will pay a fixed amount, which is the strike, quoted at the deal’s inception. Thus the net payoff to the counter parties will be the difference between these two and will be settled in cash at the expiration of the deal, though some cash payments will likely be made along the way by one or the other counter parties to maintain agreed upon margin.
Features:
The features of a variance swap include:
- the variance strike
- the realised 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:
- Nvar = variance notional (a.k.a. variance units),
= annualised realised variance, and
= variance strike