Volatility swaps (also known as variance swaps) are over-the-counter derivatives that used to hedge against the volatility risk of the underlying instruments. The underlying in this case could be foreign exchange rates, interest rates, or stock market indices.
The volatility swap will have floating volatility as one leg and fixed volatility as the other leg.
The floating leg will pay based on the volatility of the price change of the underlying asset. For example, it could be the variance of the daily log-normal returns.
The fixed leg will make a fixed payment decided at the time of entering into the swap.
The volatility swaps are usually settled in cash as the net payoff being the difference between the fixed and floating legs.
One of the most important applications of volatility swaps is in volatility trading as an alternative to using options for speculating in volatility. Variance swaps provide pure exposure to the volatility of the underlying price. This is not the case with call and put options which may carry directional risk (delta), and will require constant delta hedging. The profit and loss from a variance swap depends directly on the difference between realized and implied volatility.