Forward Volatility Agreement Hedging and Volatility Gadgets

Summary

The document defines a forward volatility agreement as exposure to the at-the-money implied volatility observed at a future date for an option expiring later. It asks how such a contract is hedged in practice. The response mentions forward-start options or straddles as possible instruments, then offers an analogy based on a paper’s volatility gadgets rather than laying out a full hedge for the agreement.

The analogy connects local volatility to a position combining a calendar spread with a short butterfly spread. A finite-difference form of the Dupire relationship motivates this construction: option-price differences across maturities and strikes are used to approximate local volatility. The document gives the formula but provides no worked example, hedge ratios, rebalancing guidance, or discussion of practical risks such as volatility-surface changes. It therefore introduces a conceptual connection and possible instruments, but does not establish a complete operational hedging method for a forward volatility agreement.

Key ideas

• A forward volatility agreement pays according to future at-the-money implied volatility relative to a strike.
• Forward-start options or straddles are mentioned as possible hedging instruments.
• The response relates local volatility to a combination of calendar and butterfly spreads.
• The finite-difference Dupire relationship motivates that spread analogy, but practical hedge details are absent.

Tags

# Hedging a FVA in practice


# 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?

## Answer by ir7 (score 0, accepted)

https://quant.stackexchange.com/a/57132

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) :

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

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.