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Impact of time–inhomogeneous jumps and leverage type effects on returns and realised variances

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  • Almut E. D. Veraart

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

Abstract

This paper studies the effect of time–inhomogeneous jumps and leverage type effects on realised variance calculations when the logarithmic asset price is given by a Lévy–driven stochastic volatility model. In such a model, the realised variance is an inconsistent estimator of the integrated variance. Nevertheless it can be used within a quasi–maximumlikelihood setup to draw inference on the model parameters. In order to do that, this paper introduces a new methodology for deriving all cumulants of the returns and realised variance in explicit form by solving a recursive system of inhomogeneous ordinary differential equations.

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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 2008-57.

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Length: 41
Date of creation: 10 Nov 2008
Date of revision:
Handle: RePEc:aah:create:2008-57

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

Related research

Keywords: Lévy processes; stochastic volatility; leverage effect; superposition; realised variance;

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References

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  1. Tim Bollerslev & Julia Litvinova & George Tauchen, 2006. "Leverage and Volatility Feedback Effects in High-Frequency Data," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(3), pages 353-384.
  2. 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.
  3. Peter Carr & Liuren Wu, 2002. "Time-Changed Levy Processes and Option Pricing," Finance 0207011, EconWPA.
  4. Veraart, Almut E.D., 2010. "Inference For The Jump Part Of Quadratic Variation Of Itô Semimartingales," Econometric Theory, Cambridge University Press, vol. 26(02), pages 331-368, April.
  5. James E. Griffin & Mark F.J. Steel, 2002. "Inference With Non-Gaussian Ornstein-Uhlenbeck Processes for Stochastic Volatility," Econometrics 0201002, EconWPA, revised 04 Apr 2003.
  6. Geman, Hélyette & Carr, Peter & Madan, Dilip B. & Yor, Marc, 2003. "Stochastic Volatility for Levy Processes," Open Access publications from Université Paris-Dauphine urn:hdl:123456789/1392, Université Paris-Dauphine.
  7. GARCIA,René & LUGER, Richard & RENAULT, Éric, 2001. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Cahiers de recherche 2001-09, Universite de Montreal, Departement de sciences economiques.
  8. Barndorff-Nielsen, Ole E. & Shephard, Neil, 2006. "Impact of jumps on returns and realised variances: econometric analysis of time-deformed Levy processes," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 217-252.
  9. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
  10. Tim Bollerslev & Hao Zhou, 2001. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Finance and Economics Discussion Series 2001-49, Board of Governors of the Federal Reserve System (U.S.).
  11. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
  12. repec:oxf:wpaper:264 is not listed on IDEAS
  13. 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.
  14. 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.
  15. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
  16. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
  17. Harvey, Andrew C & Shephard, Neil, 1996. "Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 429-34, October.
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Cited by:
  1. Almut E. D. Veraart & Luitgard A. M. Veraart, 2009. "Stochastic volatility and stochastic leverage," CREATES Research Papers 2009-20, School of Economics and Management, University of Aarhus.

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