A covariance forward contract of two underlying prices/rates. This swap pays the excess of the realized covariance between two assets (such as currencies) over a constant specified at the contract date. The seller of the swap is in fact short the covariance of the underlying assets: both the individual volatilities and the correlation between the assets. The buyer is long the covariance.

It is quite difficult to hedge this generalized form of variance swap because there is no well-established static replication formula. However, for swaps on the covariance between the absolute returns of an equity price and a currency exchange rate, the contract can be “statically” hedged using two equity quanto forwards, whilst dynamically hedging using the underlying equity and the forex rate.