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How precise is the finite sample approximation of the asymptotic distribution of realised variation measures in the presence of jumps?

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  • Almut E. D. Veraart

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

Abstract

This paper studies the impact of jumps on volatility estimation and inference based on various realised variation measures such as realised variance, realised multipower variation and truncated realised multipower variation. We review the asymptotic theory of those realised variation measures and present a new estimator for the asymptotic ‘variance’ of the centered realised variance in the presence of jumps. Next, we compare the finite sample performance of the various estimators by means of detailed Monte Carlo studies where we study the impact of the jump activity, the jump size of the jumps in the price and the presence of additional independent or dependent jumps in the volatility on the finite sample performance of the various estimators. We find that the finite sample performance of realised variance, and in particular of the log–transformed realised variance, is generally good, whereas the jump–robust statistics turn out not to be as jump robust as the asymptotic theory would suggest in the presence of a highly active jump process. In an empirical study on high frequency data from the Standard & Poor’s Depository Receipt (SPY), we investigate the impact of jumps on inference on volatility by realised variance in practice.

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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 2010-65.

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Date of creation: 18 Sep 2010
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Handle: RePEc:aah:create:2010-65

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

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Keywords: Realised variance; realised multipower variation; truncated realised variance; inference; stochastic volatility; jumps; priceLength: 48;

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References

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  1. Dennis Kristensen, 2007. "Nonparametric Filtering of the Realised Spot Volatility: A Kernel-based Approach," CREATES Research Papers 2007-02, School of Economics and Management, University of Aarhus.
  2. Vetter, Mathias & Podolskij, Mark, 2006. "Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps," Technical Reports 2006,51, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  3. Almut Veraart & Luitgard Veraart, 2012. "Stochastic volatility and stochastic leverage," Annals of Finance, Springer, vol. 8(2), pages 205-233, May.
  4. Barndorff-Nielsen, Ole E. & Hansen, Peter Reinhard & Lunde, Asger & Shephard, Neil, 2011. "Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Journal of Econometrics, Elsevier, vol. 162(2), pages 149-169, June.
  5. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 127-161, April.
  6. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 1-30.
  7. Fulvio Corsi & Davide Pirino & Roberto Renò, 2010. "Threshold bipower variation and the impact of jumps on volatility forecasting," Post-Print peer-00741630, HAL.
  8. Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, vol. 83(2), pages 413-452, February.
  9. Kim Christensen & Roel Oomen & Mark Podolskij, 2011. "Fact or friction: Jumps at ultra high frequency," CREATES Research Papers 2011-19, School of Economics and Management, University of Aarhus.
  10. Vetter, Mathias, 2010. "Limit theorems for bipower variation of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 120(1), pages 22-38, January.
  11. Almut Veraart, 2008. "Inference for the jump part of quadratic variation of Itô semimartingales," CREATES Research Papers 2008-17, School of Economics and Management, University of Aarhus.
  12. Hiroyuki Kawakatsu, 2007. "Numerical integration-based Gaussian mixture filters for maximum likelihood estimation of asymmetric stochastic volatility models," Econometrics Journal, Royal Economic Society, vol. 10(2), pages 342-358, 07.
  13. Foster, Dean P & Nelson, Daniel B, 1996. "Continuous Record Asymptotics for Rolling Sample Variance Estimators," Econometrica, Econometric Society, vol. 64(1), pages 139-74, January.
  14. Neil Shephard & Ole E. Barndorff-Nielsen, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," Economics Series Working Papers 2006-W03, University of Oxford, Department of Economics.
  15. Vetter, Mathias & Podolskij, Mark & Dette, Holger, 2004. "Estimation of integrated volatility in continuous time financial models with applications to goodness-of-fit testing," Technical Reports 2004,32, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  16. Suzanne S. Lee & Per A. Mykland, 2008. "Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics," Review of Financial Studies, Society for Financial Studies, vol. 21(6), pages 2535-2563, November.
  17. Jean Jacod & Viktor Todorov, 2010. "Do price and volatility jump together?," Papers 1010.4990, arXiv.org.
  18. 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.
  19. 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.
  20. Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 517-559, April.
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