Specifically looking at FX but i guess it's a general question. any good reference would be appreciated. FVAs are not mentioned in Derman's paper ("More than you ever wanted to Know about volatility swaps")
FVA is unrelated to Volswaps. Its stands for Forward Volatility Agreement and you are entering into a contract to buy/sell a forward starting vanilla option with black scholes parameters (with the exception of spot price) determined today.
This is used to gain exposure to forward implied volatility and is generally similar to trading a longer dated option and cutting your gamma exposure using another option with expiry equal to the forward start date, constantly re-balancing so that you are gamma flat.
In terms of sensitivity, it is similar to forward starting vol/var swaps in that you have no gamma currently and have exposure to forward vol. It is different however in that you are exposed to standard vega deformations of vanilla options as well as MTM due to skew as spot moves away from initial trade date.
As I understand it, a FVA is a swap on future implied at-the-money volatility, which is hedged by a forward starting ATM option / straddle.
I believe the idea behind this is that the future ATM IV is a proxy for expected future realised volatility. But the ATM IV, spot or future, is not a good proxy for expected realised volatility if there is substantial correlation between the underlying and the volatility.
A forward start volatility swap is really a swap on future realized volatility. See for example: