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Multiscale stochastic dynamics in finance

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  • Capobianco, Enrico

Abstract

Semimartingale probabilistic setups lead to very useful volatility estimation. The integrated volatility can be consistently estimated by the realized one according to the quadratic variation principle, even if the convergence speed can result relatively slow, depending on noise and market microstructure effects. We show, experimentally, that scale transforms based on wavelets and the corresponding cumulative periodogram estimators may offer comparable numerical performance in measuring the quadratic variation limit, thus minimizing the discrepancy between realized and integrated volatility.

Suggested Citation

  • Capobianco, Enrico, 2004. "Multiscale stochastic dynamics in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 122-127.
    • Handle: RePEc:eee:phsmap:v:344:y:2004:i:1:p:122-127
    DOI: 10.1016/j.physa.2004.06.100
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    References listed on IDEAS

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    1. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    2. Dzhaparidze, Kacha & Spreij, Peter, 1994. "Spectral characterization of the optional quadratic variation process," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 165-174, November.
    3. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
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    Cited by:

    1. Jozef Barunik & Lukas Vacha, 2015. "Realized wavelet-based estimation of integrated variance and jumps in the presence of noise," Quantitative Finance, Taylor & Francis Journals, vol. 15(8), pages 1347-1364, August.
    2. Barunik, Jozef & Krehlik, Tomas & Vacha, Lukas, 2016. "Modeling and forecasting exchange rate volatility in time-frequency domain," European Journal of Operational Research, Elsevier, vol. 251(1), pages 329-340.
    3. Wang, Fangfang, 2014. "Optimal design of Fourier estimator in the presence of microstructure noise," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 708-722.
    4. Fangfang Wang, 2016. "An Unbiased Measure of Integrated Volatility in the Frequency Domain," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(2), pages 147-164, March.
    5. Tim Leung & Theodore Zhao, 2024. "A Noisy Fractional Brownian Motion Model for Multiscale Correlation Analysis of High-Frequency Prices," Mathematics, MDPI, vol. 12(6), pages 1-21, March.

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