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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.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2008-17.

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Length: 37
Date of creation: 31 Mar 2008
Date of revision:
Handle: RePEc:aah:create:2008-17

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Web page: http://www.econ.au.dk/afn/

Related research

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

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References

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  1. 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.
  2. Posch, Olaf, 2011. "Explaining output volatility: The case of taxation," Journal of Public Economics, Elsevier, vol. 95(11), pages 1589-1606.
  3. 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.
  4. 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.
  5. 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.
  6. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous-time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323.
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Citations

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Cited by:
  1. Torben G. Andersen & Dobrislav Dobrev & Ernst Schaumburg, 2009. "Jump-Robust Volatility Estimation using Nearest Neighbor Truncation," CREATES Research Papers 2009-52, School of Economics and Management, University of Aarhus.
  2. Chevallier, Julien & Ielpo, Florian & Sévi, Benoît, 2011. "Do jumps help in forecasting the density of returns?," Economics Papers from University Paris Dauphine 123456789/6805, Paris Dauphine University.
  3. Almut Veraart & Luitgard Veraart, 2012. "Stochastic volatility and stochastic leverage," Annals of Finance, Springer, vol. 8(2), pages 205-233, May.
  4. Almut E. D. Veraart, 2010. "How precise is the finite sample approximation of the asymptotic distribution of realised variation measures in the presence of jumps?," CREATES Research Papers 2010-65, School of Economics and Management, University of Aarhus.
  5. Ole E. Barndorff–Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2010. "Ambit processes and stochastic partial differential equations," CREATES Research Papers 2010-17, School of Economics and Management, University of Aarhus.
  6. Mardi Dungey & Lyudmyla Hvozdyk, 2010. "Cojumping: Evidence from the US Treasury Bond and Futures Markets," NCER Working Paper Series 56, National Centre for Econometric Research, revised 20 Jul 2010.
  7. 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, School of Economics and Finance, revised 28 Mar 2013.
  8. Ole E. Barndorff-Nielsen & José Manuel Corcuera & Mark Podolskij, 2009. "Multipower Variation for Brownian Semistationary Processes," CREATES Research Papers 2009-21, School of Economics and Management, University of Aarhus.
  9. Ole E. Barndorff-Nielsen & Almut E. D. Veraart, 2009. "Stochastic volatility of volatility in continuous time," CREATES Research Papers 2009-25, School of Economics and Management, University of Aarhus.
  10. 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, School of Economics and Finance, revised 14 Jul 2010.
  11. Almut E. D. Veraart, 2008. "Impact of time–inhomogeneous jumps and leverage type effects on returns and realised variances," CREATES Research Papers 2008-57, School of Economics and Management, University of Aarhus.
  12. 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.
  13. Cecilia Mancini & Vanessa Mattiussi & Roberto Reno', 2012. "Spot Volatility Estimation Using Delta Sequences," Working Papers - Mathematical Economics 2012-10, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
  14. 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.

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