Volatility of Volatility and Leverage Effect from Options

ArXiv ID: 2305.04137 “View on arXiv”

Authors: Unknown

Abstract

We propose model-free (nonparametric) estimators of the volatility of volatility and leverage effect using high-frequency observations of short-dated options. At each point in time, we integrate available options into estimates of the conditional characteristic function of the price increment until the options’ expiration and we use these estimates to recover spot volatility. Our volatility of volatility estimator is then formed from the sample variance and first-order autocovariance of the spot volatility increments, with the latter correcting for the bias in the former due to option observation errors. The leverage effect estimator is the sample covariance between price increments and the estimated volatility increments. The rate of convergence of the estimators depends on the diffusive innovations in the latent volatility process as well as on the observation error in the options with strikes in the vicinity of the current spot price. Feasible inference is developed in a way that does not require prior knowledge of the source of estimation error that is asymptotically dominating.

Keywords: Volatility of Volatility, Leverage Effect, High-Frequency Data, Nonparametric Estimation, Characteristic Function, Equities (Options)

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced high-frequency econometrics, characteristic function estimation, and asymptotic theory (CLT) with non-trivial error decomposition, justifying a high math score. It demonstrates empirical validity through Monte Carlo simulations and a real-data application to S&P 500 options, indicating significant backtest-ready implementation, but remains primarily theoretical with no code or specific trading strategy provided.

  flowchart TD
    A["Research Goal<br>Estimate VoV & Leverage Effect<br>from High-Freq Options"] --> B["Input Data<br>High-Frequency Short-Dated Options"]
    
    B --> C["Methodology Step 1<br>Estimate Conditional Characteristic Function"]
    C --> D["Methodology Step 2<br>Recover Spot Volatility<br>via Inversion"]
    
    D --> E["Computational Process<br>Calculate Spot Vol Increments<br>Sample Variance & Autocovariance"]
    E --> F["Key Finding 1<br>VoV Estimator<br>Corrects Bias from Observation Errors"]
    
    D --> G["Computational Process<br>Covariance of Price & Vol Increments"]
    G --> H["Key Finding 2<br>Lev Effect Estimator<br>Model-Free Convergence Rate"]