Paper: arXiv 2510.26310
Authors: Elisa Alos, Frido Rolloos, Kenichiro Shiraya
Abstract
The covariance between the return of an asset and its realized volatility can be approximated as the difference between two specific implied volatilities. In this paper it is proved that in the small time-to-maturity limit the approximation error tends to zero. In addition a direct relation between the short time-to-maturity covariance and slope of the at-the-money implied volatility is established. The limit theorems are valid for stochastic volatility models with Hurst parameter $H \in(0, 1)$. An application of the results is to accurately approximate the Hurst parameter using only a discrete set of implied volatilities. Numerical examples under the rough Bergomi model are presented.
Complexity vs Empirical Score
- Math Complexity: 8.5/10
- Empirical Rigor: 3.5/10
- Quadrant: Lab Rats — theoretically deep, empirically untested
Why this score: The paper provides rigorous mathematical proofs using Malliavin calculus to establish limit theorems for implied volatility and Hurst parameter estimation under fractional stochastic volatility models. While mathematically strong and novel, the empirical rigor is primarily limited to synthetic Monte Carlo simulations under the rough Bergomi model without extensive real-world market backtesting or open-source code implementation.
Research Flowchart
flowchart TD
A[Goal: Estimate Hurst Parameter H from Implied Volatility] --> B[Inputs: Discrete set of implied volatilities & option prices]
B --> C[Analyze small time-to-maturity limit of zero vanna implied volatility & its dual]
C --> D[Prove approximation error approaches zero for H in 0,1]
D --> E[Establish relation between short-maturity covariance & ATM IV slope]
E --> F[Test & validate via numerical simulations under Rough Bergomi Model]
F --> G[Outcome: Accurate estimation of Hurst parameter H without full model calibration]