# Hedging a FVA in practice

A FVA (forward volatility agreement) is a forward contract on the ATM implied volatility. So at at maturity date $$T$$ the payoff of a FVA with unit notional is $$(I_{ATM}(T,T') - K)$$ where $$I_{ATM}(T,T')$$ is the ATM (or ATM forward) implied volatility at $$T$$ of a vanilla option with maturity $$T'$$.

How are these contracts hedged in practice?

Other than forward start options/straddles, this might help too: there is an interesting analogy between $$[S,T]$$-forward interest rate exposure related to short $$S$$-maturity zero coupon bond/long $$T$$-maturity zero coupon bond position and local volatility related to long calendar spread/short butterfly spread position in this Derman, Kani, and Kamal paper ('volatility gadgets'). The finite difference form of Dupire formula suggests the latter relation (formula (4) in the paper) :
$$\sigma(K,T) = \frac{2\left(C(K,T) - C(K,T-\delta T) \right)(\delta T)^{-1}}{\left(C(K+\delta K,T-\delta T) - 2C(K,T-\delta T) + C(K-\delta K,T-\delta T) \right)(\delta K)^{2}K^{-2}}$$