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Inference for Realized Quadratic Covariation of R and R2 as a Measure of Return Asymmetry

  • Haozhe Jiang
  • Ostap Okhrin
  • Michael Rockinger
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Abstract

We propose a nonparametric test of return asymmetry based on the realized quadratic covariation between a cumulative return path and its square using high-frequency data. Our null hypothesis is that the volatility path is independent of the Brownian motion driving returns. Under this null and a martingale condition, the infill limit of the statistic is conditionally Gaussian given the volatility path, with a conditional variance determined by integrated variance. Studentization by a feasible variance estimator yields an asymptotically standard normal statistic without specifying a parametric model for volatility. Simulations under Heston and Bates dynamics show near-nominal per-window size, quantify power gains from independent-window aggregation, and assess sensitivity to jump removal and volatility-dependent drift. An application to 165 U.S. stocks over 1998--2025 finds that rejections concentrate in negative asymmetry, consistent with the leverage effect.

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Cite

BibTeXRIS
BibTeX
@misc{jiang2026inference,
  title = {{Inference for Realized Quadratic Covariation of $R$ and $R^2$ as a Measure of Return Asymmetry}},
  author = {Haozhe Jiang and Ostap Okhrin and Michael Rockinger},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06368},
  eprint = {2611.06368},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06368},
}
RIS
TY  - UNPB
TI  - Inference for Realized Quadratic Covariation of R and R^2 as a Measure of Return Asymmetry
AU  - Haozhe Jiang
AU  - Ostap Okhrin
AU  - Michael Rockinger
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06368
UR  - https://arxiv.org/abs/2611.06368
AB  - We propose a nonparametric test of return asymmetry based on the realized quadratic covariation between a cumulative return path and its square using high-frequency data. Our null hypothesis is that the volatility path is independent of the Brownian motion driving returns. Under this null and a martingale condition, the infill limit of the statistic is conditionally Gaussian given the volatility path, with a conditional variance determined by integrated variance. Studentization by a feasible variance estimator yields an asymptotically standard normal statistic without specifying a parametric model for volatility. Simulations under Heston and Bates dynamics show near-nominal per-window size, quantify power gains from independent-window aggregation, and assess sensitivity to jump removal and volatility-dependent drift. An application to 165 U.S. stocks over 1998--2025 finds that rejections concentrate in negative asymmetry, consistent with the leverage effect.
ER  -