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Inference for the jump part of quadratic variation of Itô semimartingales

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  • Almut Veraart

    () (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

Recent research has focused on modelling asset prices by Itô semimartingales. In such a modelling framework, the quadratic variation consists of a continuous and a jump component. This paper is about inference on the jump part of the quadratic variation, which can be estimated by the difference of realised variance and realised multipower variation. The main contribution of this paper is twofold. First, it provides a bivariate asymptotic limit theory for realised variance and realised multipower variation in the presence of jumps. Second, this paper presents new, consistent estimators for the jump part of the asymptotic variance of the estimation bias. Eventually, this leads to a feasible asymptotic theory which is applicable in practice. Finally, Monte Carlo studies reveal a good finite sample performance of the proposed feasible limit theory.

Suggested Citation

  • Almut Veraart, 2008. "Inference for the jump part of quadratic variation of Itô semimartingales," CREATES Research Papers 2008-17, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2008-17
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    References listed on IDEAS

    as
    1. Xin Huang & George Tauchen, 2005. "The Relative Contribution of Jumps to Total Price Variance," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(4), pages 456-499.
    2. Ole BARNDORFF-NIELSEN & Svend Erik GRAVERSEN & Jean JACOD & Mark PODOLSKIJ & Neil SHEPHARD, 2004. "A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales," OFRC Working Papers Series 2004fe21, Oxford Financial Research Centre.
    3. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous-time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323.
    4. Barndorff-Nielsen, Ole E. & Graversen, Svend Erik & Jacod, Jean & Shephard, Neil, 2006. "Limit Theorems For Bipower Variation In Financial Econometrics," Econometric Theory, Cambridge University Press, vol. 22(04), pages 677-719, August.
    5. Posch, Olaf, 2011. "Explaining output volatility: The case of taxation," Journal of Public Economics, Elsevier, vol. 95(11), pages 1589-1606.
    6. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
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    Citations

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    Cited by:

    1. Andersen, Torben G. & Dobrev, Dobrislav & Schaumburg, Ernst, 2012. "Jump-robust volatility estimation using nearest neighbor truncation," Journal of Econometrics, Elsevier, vol. 169(1), pages 75-93.
    2. Almut Veraart & Luitgard Veraart, 2012. "Stochastic volatility and stochastic leverage," Annals of Finance, Springer, vol. 8(2), pages 205-233, May.
    3. Almut E. D. Veraart, 2008. "Impact of time–inhomogeneous jumps and leverage type effects on returns and realised variances," CREATES Research Papers 2008-57, Department of Economics and Business Economics, Aarhus University.
    4. Dungey, Mardi & Hvozdyk, Lyudmyla, 2012. "Cojumping: Evidence from the US Treasury bond and futures markets," Journal of Banking & Finance, Elsevier, vol. 36(5), pages 1563-1575.
    5. Per A. Mykland & Neil Shephard & Kevin Sheppard, 2012. "Efficient and feasible inference for the components of financial variation using blocked multipower variation," Economics Papers 2012-W02, Economics Group, Nuffield College, University of Oxford.
    6. Cecilia Mancini & Vanessa Mattiussi & Roberto Renò, 2015. "Spot volatility estimation using delta sequences," Finance and Stochastics, Springer, vol. 19(2), pages 261-293, April.
    7. Ole E. Barndorff-Nielsen & José Manuel Corcuera & Mark Podolskij, 2009. "Multipower Variation for Brownian Semistationary Processes," CREATES Research Papers 2009-21, Department of Economics and Business Economics, Aarhus University.
    8. Almut Veraart, 2011. "How precise is the finite sample approximation of the asymptotic distribution of realised variation measures in the presence of jumps?," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(3), pages 253-291, September.
    9. Zu, Yang & Peter Boswijk, H., 2014. "Estimating spot volatility with high-frequency financial data," Journal of Econometrics, Elsevier, vol. 181(2), pages 117-135.
    10. Markus Bibinger & Mathias Vetter, 2015. "Estimating the quadratic covariation of an asynchronously observed semimartingale with jumps," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(4), pages 707-743, August.
    11. repec:dau:papers:123456789/6805 is not listed on IDEAS
    12. Ole E. Barndorff-Nielsen & Almut E. D. Veraart, 2009. "Stochastic volatility of volatility in continuous time," CREATES Research Papers 2009-25, Department of Economics and Business Economics, Aarhus University.
    13. Markus Bibinger & Mathias Vetter, 2013. "Estimating the quadratic covariation of an asynchronously observed semimartingale with jumps," SFB 649 Discussion Papers SFB649DP2013-029, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    14. Ole E. Barndorff–Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2010. "Ambit processes and stochastic partial differential equations," CREATES Research Papers 2010-17, Department of Economics and Business Economics, Aarhus University.
    15. Dungey, Mardi & Hvozdyk, Lyudmyla, 2010. "Cojumping: Evidence from the US Treasury Bond and Future Markets (Discussion Paper 2010-06)," Working Papers 10450, University of Tasmania, Tasmanian School of Business and Economics, revised 14 Jul 2010.
    16. Dungey, Mardi & Henry, Olan T & Hvodzdyk, Lyudmyla, 2013. "The impact of jumps and thin trading on realized hedge ratios," Working Papers 2013-02, University of Tasmania, Tasmanian School of Business and Economics, revised 28 Mar 2013.

    More about this item

    Keywords

    Quadratic variation; Itô semimartingale; stochastic volatility; jumps; realised variance; realised multipower variation; high–frequency data;

    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
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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