A variance swap can be used to hedge tail risk. One counterparty (Sally the trader, in this example) pays a forward (fixed) variance in exchange for a future, REALIZED variance. So she is "long volatility" and will profit if the realized variance is greater than expected. The advantage of a variance (or volatility) swap is the relatively pure bet on volatility; e.g., it is not a directional bet on price and lacks some of the Greek exposures of (eg) an option. You can get the spreadsheet I wrote for this on our website!