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Global estimation of realized spot volatility in the presence of price jumps

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  • Dare, Wale
  • Fengler, Matthias

Abstract

We propose a non-parametric procedure for estimating the realized spot volatility of a price process described by an Itô semimartingale with Lévy jumps. The procedure integrates the threshold jump elimination technique of Mancini (2009) with a frame (Gabor) expansion of the realized trajectory of spot volatility. We show that the procedure converges in probability in L2([0, T]) for a wide class of spot volatility processes, including those with discontinuous paths. Our analysis assumes the time interval between price observations tends to zero; as a result, the intended application is for the analysis of high frequency financial data.

Suggested Citation

  • Dare, Wale & Fengler, Matthias, 2017. "Global estimation of realized spot volatility in the presence of price jumps," Economics Working Paper Series 1715, University of St. Gallen, School of Economics and Political Science.
    • Handle: RePEc:usg:econwp:2017:15
    as

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    File URL: http://ux-tauri.unisg.ch/RePEc/usg/econwp/EWP-1715.pdf
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    References listed on IDEAS

    as
    1. Cecilia Mancini, 2009. "Non‐parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 270-296, June.
    2. Maria Elvira Mancino & Paul Malliavin, 2002. "Fourier series method for measurement of multivariate volatilities," Finance and Stochastics, Springer, vol. 6(1), pages 49-61.
    3. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics," Econometrica, Econometric Society, vol. 72(3), pages 885-925, May.
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    More about this item

    Keywords

    Nonparametric estimation; Itô semimartingale; Lévy jumps; Gabor frames; realized spot volatility;
    All these keywords.

    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

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