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Estimating the Spot Covariation of Asset Prices – Statistical Theory and Empirical Evidence

Author

Listed:
  • Markus Bibinger
  • Nikolaus Hautsch
  • Peter Malec
  • Markus Reiss
Abstract
We propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semimartingale log asset price process which is subject to noise and non-synchronous observations. The estimator is constructed based on a local average of block-wise parametric spectral covariance estimates. The latter originate from a local method of moments (LMM) which recently has been introduced by Bibinger et al. (2014). We extend the LMM estimator to allow for autocorrelated noise and propose a method to adaptively infer the autocorrelations from the data. We prove the consistency and asymptotic normality of the proposed spot covariance estimator. Based on extensive simulations we provide empirical guidance on the optimal implementation of the estimator and apply it to high-frequency data of a cross-section of NASDAQ blue chip stocks. Employing the estimator to estimate spot covariances, correlations and betas in normal but also extreme-event periods yields novel insights into intraday covariance and correlation dynamics. We show that intraday (co-)variations (i) follow underlying periodicity patterns, (ii) reveal substantial intraday variability associated with (co-)variation risk, (iii) are strongly serially correlated, and (iv) can increase strongly and nearly instantaneously if new information arrives.

Suggested Citation

  • Markus Bibinger & Nikolaus Hautsch & Peter Malec & Markus Reiss, 2014. "Estimating the Spot Covariation of Asset Prices – Statistical Theory and Empirical Evidence," Cambridge Working Papers in Economics 1464, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:1464
    Note: pm563
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    2. Mustafayeva, Konul & Wang, Weining, 2020. "Non-Parametric Estimation of Spot Covariance Matrix with High-Frequency Data," IRTG 1792 Discussion Papers 2020-025, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    3. Žikica Lukić & Bojana Milošević, 2024. "A novel two-sample test within the space of symmetric positive definite matrix distributions and its application in finance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(5), pages 797-820, October.
    4. Bibinger, Markus & Madensoy, Mehmet, 2019. "Change-point inference on volatility in noisy Itô semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 4878-4925.
    5. Todorov, Viktor & Zhang, Yang, 2023. "Bias reduction in spot volatility estimation from options," Journal of Econometrics, Elsevier, vol. 234(1), pages 53-81.
    6. Jacod, Jean & Mykland, Per A., 2015. "Microstructure noise in the continuous case: Approximate efficiency of the adaptive pre-averaging method," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 2910-2936.
    7. Rui Da & Dacheng Xiu, 2021. "When Moving‐Average Models Meet High‐Frequency Data: Uniform Inference on Volatility," Econometrica, Econometric Society, vol. 89(6), pages 2787-2825, November.
    8. Zhang, Congshan & Li, Jia & Bollerslev, Tim, 2022. "Occupation density estimation for noisy high-frequency data," Journal of Econometrics, Elsevier, vol. 227(1), pages 189-211.
    9. Torben G. Andersen & Martin Thyrsgaard & Viktor Todorov, 2021. "Recalcitrant betas: Intraday variation in the cross‐sectional dispersion of systematic risk," Quantitative Economics, Econometric Society, vol. 12(2), pages 647-682, May.
    10. Bibinger, Markus & Neely, Christopher & Winkelmann, Lars, 2019. "Estimation of the discontinuous leverage effect: Evidence from the NASDAQ order book," Journal of Econometrics, Elsevier, vol. 209(2), pages 158-184.
    11. repec:hum:wpaper:sfb649dp2014-037 is not listed on IDEAS
    12. Bibinger, Markus & Winkelmann, Lars, 2014. "Common price and volatility jumps in noisy high-frequency data," SFB 649 Discussion Papers 2014-037, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    13. Siem Jan Koopman & Rutger Lit & André Lucas & Anne Opschoor, 2018. "Dynamic discrete copula models for high‐frequency stock price changes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(7), pages 966-985, November.
    14. Hautsch, Nikolaus & Horvath, Akos, 2019. "How effective are trading pauses?," Journal of Financial Economics, Elsevier, vol. 131(2), pages 378-403.
    15. Giuseppe Buccheri & Giacomo Bormetti & Fulvio Corsi & Fabrizio Lillo, 2018. "A Score-Driven Conditional Correlation Model for Noisy and Asynchronous Data: an Application to High-Frequency Covariance Dynamics," Papers 1803.04894, arXiv.org, revised Mar 2019.
    16. Tobias Eckernkemper & Bastian Gribisch, 2021. "Intraday conditional value at risk: A periodic mixed‐frequency generalized autoregressive score approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(5), pages 883-910, August.
    17. Dalderop, Jeroen, 2020. "Nonparametric filtering of conditional state-price densities," Journal of Econometrics, Elsevier, vol. 214(2), pages 295-325.
    18. Chae-Deug, Yi, 2024. "Realized normal volatility and maximum outlying jumps in high frequency returns for Korean won–US Dollar," International Review of Financial Analysis, Elsevier, vol. 95(PA).
    19. Kim Christensen & Ulrich Hounyo & Zhi Liu, 2024. "A nonparametric test for diurnal variation in spot correlation processes," Papers 2408.02757, arXiv.org.
    20. Richard Y. Chen, 2019. "The Fourier Transform Method for Volatility Functional Inference by Asynchronous Observations," Papers 1911.02205, arXiv.org.
    21. Markus Bibinger & Nikolaus Hautsch & Alexander Ristig, 2024. "Jump detection in high-frequency order prices," Papers 2403.00819, arXiv.org.
    22. Jir^o Akahori & Nien-Lin Liu & Maria Elvira Mancino & Tommaso Mariotti & Yukie Yasuda, 2023. "Symmetric positive semi-definite Fourier estimator of instantaneous variance-covariance matrix," Papers 2304.04372, arXiv.org.
    23. Jakob Albers & Mihai Cucuringu & Sam Howison & Alexander Y. Shestopaloff, 2021. "Fragmentation, Price Formation, and Cross-Impact in Bitcoin Markets," Papers 2108.09750, arXiv.org.

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    More about this item

    Keywords

    local method of moments; spot covariance; smoothing; intraday (co-)variation risk;
    All these keywords.

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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