A nonparametric test for rough volatility

ArXiv ID: 2407.10659 “View on arXiv”

Authors: Unknown

Abstract

We develop a nonparametric test for deciding whether volatility of an asset follows a standard semimartingale process, with paths of finite quadratic variation, or a rough process with paths of infinite quadratic variation. The test utilizes the fact that volatility is rough if and only if volatility increments are negatively autocorrelated at high frequencies. It is based on the sample autocovariance of increments of spot volatility estimates computed from high-frequency asset return data. By showing a feasible CLT for this statistic under the null hypothesis of semimartingale volatility paths, we construct a test with fixed asymptotic size and an asymptotic power equal to one. The test is derived under very general conditions for the data-generating process. In particular, it is robust to jumps with arbitrary activity and to the presence of market microstructure noise. In an application of the test to SPY high-frequency data, we find evidence for rough volatility.

Keywords: Rough Volatility, Semimartingale Test, High-Frequency Data, Autocovariance, Market Microstructure Noise, Equities

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced stochastic calculus, central limit theorems, and high-frequency econometrics with heavy formal proofs and abstract probability theory, giving it high math complexity. It demonstrates strong empirical rigor through the application of the test to real high-frequency SPY data, robustness to market microstructure noise and jumps, and discussion of finite-sample performance.

  flowchart TD
    A["Research Goal\nDetermine if volatility is\nRough or Semimartingale"] --> B["Key Methodology\nCompute sample autocovariance\nof spot volatility increments"]
    B --> C["Data Inputs\nHigh-frequency asset returns\nSPY data"]
    C --> D["Computational Processes\nFeasible CLT under Null\nRobust to jumps & noise"]
    D --> E["Key Findings\nEvidence of Rough Volatility\nin SPY data"]