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A nonparametric test for rough volatility

Carsten H. Chong, Viktor Todorov

arXiv 15 Jul 2024 · Mathematics — Statistics Theory · publishedJournal of the American Statistical Association (2025) · 4 citations (OpenAlex)

arXiv:2407.10659 · PDF · DOI · OpenAlex · Extracted main text

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.

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45
references
63
in-text mentions
45
distinct cited
3
self-citations
39,919
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1J. Jacod and P. Protter (2012) Discretization of Processes, volume 67 of Stochastic Modelling and Applied Probability1.00075100%
2J. Gatheral, T. Jaisson, and M. Rosenbaum (2018) Volatility is rough0.84333100%
3M. Bennedsen, A. Lunde, and M. S. Pakkanen (2022) Decoupling the short- and long-term behavior of stochastic volatility0.81142100%
4J. Jacod and A. N. Shiryaev (2003) Limit Theorems for Stochastic Processes, volume 288 of Grundlehren der mathematischen Wissenschaften [Fundamental Principles of…0.64422100%
5X. Wang, W. Xiao, and J. Yu (2023) Modeling and forecasting realized volatility with the fractional Ornstein–Uhlenbeck process0.64422100%
6O. E. Barndorff-Nielsen, J. M. Corcuera, and M. Podolskij (2011) Multipower variation for Brownian semistationary processes0.64422100%
7R. Cont and P. Das (2024) Rough volatility: Fact or artefact?0.64422100%
8C. H. Chong and V. Todorov (2024) A nonparametric test for rough volatility self0.64422100%
9X. Liu, S. Shi, and J. Yu (2020) Persistent and rough volatility0.51121100%
10Y. S. Mishura (2008) Stochastic Calculus for Fractional Brownian Motion and Related Processes, volume 1929 of Lecture Notes in Mathematics0.51121100%

Showing the top 10 of 45 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Optimal Estimation for General Gaussian Processes0.40511
2Spectral analysis of high-dimensional spot volatility matrix with applications0.40511