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Spot volatility estimation using delta sequences

Author

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  • Cecilia Mancini

    ()

  • Vanessa Mattiussi

    ()

  • Roberto Renò

    ()

Abstract

We introduce a unifying class of nonparametric spot volatility estimators based on delta sequences and conceived to include many of the existing estimators in the field as special cases. The full limit theory is first derived when unevenly sampled observations under infill asymptotics and fixed time horizon are considered, and the state variable is assumed to follow a Brownian semimartingale. We then extend our class of estimators to include Poisson jumps or financial microstructure noise in the observed price process. This work makes different approaches (kernels, wavelets, Fourier) comparable. For example, we explicitly illustrate some drawbacks of the Fourier estimator. Specific delta sequences are applied to data from the S&P 500 stock index futures market. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Cecilia Mancini & Vanessa Mattiussi & Roberto Renò, 2015. "Spot volatility estimation using delta sequences," Finance and Stochastics, Springer, vol. 19(2), pages 261-293, April.
  • Handle: RePEc:spr:finsto:v:19:y:2015:i:2:p:261-293
    DOI: 10.1007/s00780-015-0255-1
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    References listed on IDEAS

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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Kanaya, Shin & Kristensen, Dennis, 2016. "Estimation Of Stochastic Volatility Models By Nonparametric Filtering," Econometric Theory, Cambridge University Press, vol. 32(04), pages 861-916, August.
    2. repec:eee:ecofin:v:44:y:2018:i:c:p:62-79 is not listed on IDEAS
    3. Chao Yu & Yue Fang & Zeng Li & Bo Zhang & Xujie Zhao, 2014. "Non-Parametric Estimation Of High-Frequency Spot Volatility For Brownian Semimartingale With Jumps," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(6), pages 572-591, November.
    4. repec:eee:spapps:v:128:y:2018:i:6:p:1958-1987 is not listed on IDEAS
    5. repec:eee:ecosta:v:6:y:2018:i:c:p:22-43 is not listed on IDEAS
    6. Ghysels, Eric, 2014. "Factor Analysis with Large Panels of Volatility Proxies," CEPR Discussion Papers 10034, C.E.P.R. Discussion Papers.
    7. Zu, Yang & Peter Boswijk, H., 2014. "Estimating spot volatility with high-frequency financial data," Journal of Econometrics, Elsevier, vol. 181(2), pages 117-135.

    More about this item

    Keywords

    Spot volatility; High-frequency data; Microstructure noise; Dirac delta; Fourier estimator; 91G70; C13; C14; C22; G1;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G1 - Financial Economics - - General Financial Markets

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