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Modeling volatility for high-frequency data with rounding error: a nonparametric Bayesian approach

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Abstract

Rounding is a pivotal source of market microstructure noise which should be carefully addressed in high-frequency data analysis. This study incorporates available market information in modeling rounding errors and proposes a Rounding Error-Trading Information model from the Bayesian perspective. We assign a thresholded Gaussian process prior to the instantaneous volatility of the log-price process and adopt a fully Bayesian approach with an efficient Markov chain Monte Carlo algorithm for model inference, based on which a novel Trading Information-based estimator for the integrated volatility is provided. Simulation studies show that the proposed method can effectively recover the true latent log-prices, instantaneous volatility, and integrated volatility with multiple volatility shapes and rounding mechanisms, even under model misspecification. Extensive empirical studies show that the rounding mechanism in the Shanghai A-share market is likely to be random and the trading directions have a greater impact on the rounding results of the asset prices than the true latent log-prices, which is a consistent finding with that in the literature.

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Acknowledgements

The research of Bo Zhang is supported by National Natural Science Foundation of China (NSFC, 72271232, 71873137) and the MOE project of key research institute of Humanities and Social Sciences (22JJD110001). The research of Ben Wu is supported by National Natural Science Foundation of China (NSFC, 12201628). The authors gratefully acknowledge the support of Public Computing Cloud, Renmin University of China.

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  1. Ben Wu and Bo Zhang have contributed equally to this paper.

Authors and Affiliations

  1. Center for Applied Statistics, School of Statistics, Renmin University of China at Beijing, 59 Zhongguancun Street, Beijing, 100872, China

    Wanwan Liang, Ben Wu & Bo Zhang

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  1. Wanwan Liang
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  2. Ben Wu
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  3. Bo Zhang
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All authors contributed to the study conception and design. The first draft of the manuscript was written by Wanwan Liang and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Ben Wu or Bo Zhang.

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Liang, W., Wu, B. & Zhang, B. Modeling volatility for high-frequency data with rounding error: a nonparametric Bayesian approach. Stat Comput 34, 23 (2024). https://doi.org/10.1007/s11222-023-10341-0

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