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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?

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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) :

$$ \sigma(K,T) = \frac{2\left(C(K,T) - C(K,T-\delta T) \right)(\delta T)^{-1}}{\left(C(K+\delta K,T-\delta T) - 2C(K,T-\delta T) + C(K-\delta K,T-\delta T) \right)(\delta K)^{2}K^{-2}}$$

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  • $\begingroup$ Thanks! I almost wanted to ask well how are forward start options hedged, but I guess that would be a chicken or egg type of question. $\endgroup$ Aug 5 '20 at 14:55

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