Estimating the Hurst parameter from the zero vanna implied volatility and its dual

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Highly relevant for quantitative trading in options markets. The paper provides a model-free method to estimate the Hurst parameter from implied volatility surfaces, which is crucial for calibrating rough volatility models used in modern quantitative finance. The zero vanna implied volatility difference provides a direct link to the covariance between returns and volatility, useful for skew trading strategies and volatility risk management. The method avoids the need for illiquid volatility swaps and does not require full model calibration.

The theoretical framework (Malliavin calculus proofs) is mathematically sophisticated but the practical implementation is relatively straightforward: one needs to identify zero vanna and dual zero vanna strikes from the implied volatility surface, compute their IV difference, and apply the scaling formula. The Monte Carlo simulation for validation requires implementing the rough Bergomi model with fractional Brownian motion, which involves careful discretization. The Hurst parameter estimation formula (1.3) is simple to implement given IV data at two maturities.

The paper provides detailed mathematical proofs in the appendix, specifies model parameters for numerical experiments (S0=100, σ0=0.2, α=0.8, various ρ and H values), and describes the Monte Carlo setup (20 million simulations, max{500T,100} time steps). However, no code or data repository is provided. The rough Bergomi model is well-documented in literature, enabling reproduction of numerical results.