Resolve the measurement of structural volatility against an appropriate forward-looking benchmark

Determine an appropriate measurement of the structural volatility parameter underlying the fee implied volatility proxy, including how it should be benchmarked against a genuine forward-looking volatility measure rather than backward-looking realized volatility.

Background

The paper defines a fee implied volatility proxy from Uniswap pool fee rate, trading volume, and active liquidity, but emphasizes that this quantity is not structurally identified as Black–Scholes implied volatility. The omitted hedging-cost component depends on the external price process and arbitrage timing, while realized volatility is backward-looking and may not represent the forward-looking structural volatility parameter.

The empirical comparison uses realized volatility as an imperfect benchmark and shows that the resulting realized-volatility-referenced capture ratio is unstable. The paper therefore identifies the choice of an appropriate benchmark for the latent structural volatility as an unresolved measurement issue.

References

This sharpens rather than weakens the identification gap in Section \ref{sec:not-identified}: not only does $\widehat{\alpha}{\mathrm{RV}(t)$ fail to sit at a fixed value, its relationship to the theoretical bound on $\alpha$ depends entirely on which benchmark is used to stand in for $\sigma\ast$, which is itself an unresolved measurement choice.

— Fee Implied Volatility on Uniswap v3: A DEX Native Proxy and Its Limits  (2608.13340 - Khaldoun, 13 Aug 2026) in Section 6.1, subsection “Empirical illustration on the ETH/USDC 30bps pool”