A variation on variance swaps which weights the periodic squared return of the underlying by the ratio of current price to initial price. That is, it pays at maturity the weighted variance of the underlying. The weight is given by the underlying level normalized by the underlying level at initiation. The gamma swap obviates the need for embedding a cap which otherwise is usually embedded in volatility swaps or variance swaps to protect the seller from the impact of volatility or variance spike, following an underlying price crash. In other words, if the price in current period crashes (approaches zero), the squared return would be extremely large, but the weighted return would approach zero. To limit the losses that could arise from a decreasing current price and tap into the potential of a rising current price, an investor can buy a gamma swap and sell a variance swap.

The gamma swap, like its closest cousin, the entropy swap, is naturally exposed to correlation between the underlying price and volatility. Gamma swaps can be used in trading index volatility against the combined individual volatilities. The gamma swap is also known as a weighted variance swap.