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Some recent developments in stochastic volatility modelling

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  • Ole E. Barndorff-Nielsen

    ()
    (The Centre for Mathematical Physics and Stochastics (MaPhySto), University of Aarhus)

  • Elisa Nicolato

    ()
    (Dept of Mathematical Sciences, University of Aarhus)

  • Neil Shephard

    ()
    (Nuffield College, Oxford)

Abstract

This paper reviews and puts in context some of our recent work on stochastic volatility modelling for financial economics. Here our main focus is on: (i) the relationship between subordination and stochastic volatility, (ii) OU based volatility models, (iii) exact option pricing, (iv) realised power variation and realised variance, (v) building multivariate models.

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File URL: http://www.nuff.ox.ac.uk/Economics/papers/2001/w25/qf.pdf
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Bibliographic Info

Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2001-W25.

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Length: 23 pages
Date of creation: 07 Dec 2001
Date of revision:
Handle: RePEc:nuf:econwp:0125

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Web page: http://www.nuff.ox.ac.uk/economics/

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References

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  1. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
  2. Neil Shephard, 2005. "Stochastic volatility," Economics Series Working Papers, University of Oxford, Department of Economics 2005-W17, University of Oxford, Department of Economics.
  3. Kramkov, D.O., 1994. "Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets," Discussion Paper Serie B, University of Bonn, Germany 294, University of Bonn, Germany.
  4. Ola Elerian & Siddhartha Chib & Neil Shephard, 2000. "Likelihood inference for discretely observed non-linear diffusions," OFRC Working Papers Series, Oxford Financial Research Centre 2000mf02, Oxford Financial Research Centre.
  5. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," Center for Financial Institutions Working Papers, Wharton School Center for Financial Institutions, University of Pennsylvania 99-08, Wharton School Center for Financial Institutions, University of Pennsylvania.
  6. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, Elsevier, vol. 61(1), pages 43-76, July.
  7. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "How accurate is the asymptotic approximation to the distribution of realised volatility?," Economics Papers, Economics Group, Nuffield College, University of Oxford 2001-W16, Economics Group, Nuffield College, University of Oxford.
  8. Gareth O. Roberts & Omiros Papaspiliopoulos & Petros Dellaportas, 2004. "Bayesian inference for non-Gaussian Ornstein-Uhlenbeck stochastic volatility processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, Royal Statistical Society, vol. 66(2), pages 369-393.
  9. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, Elsevier, vol. 50(2), pages 125-150, November.
  10. Rüdiger Frey & Carlos A. Sin, 1999. "Bounds on European Option Prices under Stochastic Volatility," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(2), pages 97-116.
  11. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers, Economics Group, Nuffield College, University of Oxford 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
  12. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Realised power variation and stochastic volatility models," Economics Papers, Economics Group, Nuffield College, University of Oxford 2001-W18, Economics Group, Nuffield College, University of Oxford.
  13. Darrell Duffie & Jun Pan & Kenneth Singleton, 1999. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," NBER Working Papers 7105, National Bureau of Economic Research, Inc.
  14. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, Royal Statistical Society, vol. 63(2), pages 167-241.
  15. Ernst Eberlein & Sebastian Raible, 1999. "Term Structure Models Driven by General Lévy Processes," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(1), pages 31-53.
  16. N. Bellamy & M. Jeanblanc, 2000. "Incompleteness of markets driven by a mixed diffusion," Finance and Stochastics, Springer, Springer, vol. 4(2), pages 209-222.
  17. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 7(2), pages 211-239.
  18. Ernst Eberlein & Jean Jacod, 1997. "On the range of options prices (*)," Finance and Stochastics, Springer, Springer, vol. 1(2), pages 131-140.
  19. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Normal modified stable processes," Economics Papers, Economics Group, Nuffield College, University of Oxford 2001-W6, Economics Group, Nuffield College, University of Oxford.
  20. Francis X. Diebold & Marc Nerlove, 1986. "The dynamics of exchange rate volatility: a multivariate latent factor ARCH model," Special Studies Papers, Board of Governors of the Federal Reserve System (U.S.) 205, Board of Governors of the Federal Reserve System (U.S.).
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Citations

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Cited by:
  1. Meddahi, N., 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 2001-26, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. James E. Griffin & Mark F.J. Steel, 2002. "Inference With Non-Gaussian Ornstein-Uhlenbeck Processes for Stochastic Volatility," Econometrics, EconWPA 0201002, EconWPA, revised 04 Apr 2003.
  3. Nour Meddahi, 2003. "ARMA representation of integrated and realized variances," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 6(2), pages 335-356, December.
  4. Fasen, Vicky, 2013. "Statistical estimation of multivariate Ornstein–Uhlenbeck processes and applications to co-integration," Journal of Econometrics, Elsevier, Elsevier, vol. 172(2), pages 325-337.
  5. Ole E. Barndorff-Nielsen & Neil Shephard, 2002. "Power Variation and Time Change," Economics Papers, Economics Group, Nuffield College, University of Oxford 2002-W24, Economics Group, Nuffield College, University of Oxford.
  6. Friedrich Hubalek & Petra Posedel, 2008. "Asymptotic analysis for a simple explicit estimator in Barndorff-Nielsen and Shephard stochastic volatility models," Papers 0807.3479, arXiv.org.
  7. Friedrich Hubalek & Martin Keller-Ressel & Carlo Sgarra, 2014. "Geometric Asian Option Pricing in General Affine Stochastic Volatility Models with Jumps," Papers 1407.2514, arXiv.org.
  8. Sergei Levendorskii, 2002. "Pseudo-diffusions and Quadratic term structure models," Papers cond-mat/0212249, arXiv.org, revised Apr 2004.
  9. Alexander Bade & Gabriel Frahm & Uwe Jaekel, 2009. "A general approach to Bayesian portfolio optimization," Computational Statistics, Springer, Springer, vol. 70(2), pages 337-356, October.
  10. Di Nunno, Giulia & Sjursen, Steffen, 2014. "BSDEs driven by time-changed Lévy noises and optimal control," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 124(4), pages 1679-1709.
  11. Tomáš Tichý, 2006. "Model Dependency of the Digital Option Replication – Replication under an Incomplete Model (in English)," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, Charles University Prague, Faculty of Social Sciences, vol. 56(7-8), pages 361-379, July.

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