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Some recent developments in stochastic volatility modelling

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  • Neil Shephard
  • Ole E. Barndorff-Nielsen

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 University of Oxford, Department of Economics in its series Economics Series Working Papers with number 2001-W25.

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Date of creation: 01 Dec 2001
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Handle: RePEc:oxf:wpaper:2001-w25

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References

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  1. 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.
  2. 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, vol. 66(2), pages 369-393.
  3. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
  4. 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, vol. 63(2), pages 167-241.
  5. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  6. Kramkov, D.O., 1994. "Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets," Discussion Paper Serie B 294, University of Bonn, Germany.
  7. Torben Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," NBER Working Papers 6961, National Bureau of Economic Research, Inc.
  8. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239.
  9. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "How accurate is the asymptotic approximation to the distribution of realised volatility?," Economics Papers 2001-W16, Economics Group, Nuffield College, University of Oxford.
  10. Ernst Eberlein & Jean Jacod, 1997. "On the range of options prices (*)," Finance and Stochastics, Springer, vol. 1(2), pages 131-140.
  11. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, vol. 50(2), pages 125-150, November.
  12. Elerian, O. & Chib, S. & Shephard, N., 1998. "Likelihood INference for Discretely Observed Non-linear Diffusions," Economics Papers 146, Economics Group, Nuffield College, University of Oxford.
  13. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280.
  14. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Realised power variation and stochastic volatility models," Economics Papers 2001-W18, Economics Group, Nuffield College, University of Oxford.
  15. Francis X. Diebold & Marc Nerlove, 1986. "The dynamics of exchange rate volatility: a multivariate latent factor ARCH model," Special Studies Papers 205, Board of Governors of the Federal Reserve System (U.S.).
  16. Rüdiger Frey & Carlos A. Sin, 1999. "Bounds on European Option Prices under Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 97-116.
  17. 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.
  18. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Normal modified stable processes," Economics Papers 2001-W6, Economics Group, Nuffield College, University of Oxford.
  19. N. Bellamy & M. Jeanblanc, 2000. "Incompleteness of markets driven by a mixed diffusion," Finance and Stochastics, Springer, vol. 4(2), pages 209-222.
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Citations

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Cited by:
  1. Fasen, Vicky, 2013. "Statistical estimation of multivariate Ornstein–Uhlenbeck processes and applications to co-integration," Journal of Econometrics, Elsevier, vol. 172(2), pages 325-337.
  2. Sergei Levendorskii, 2002. "Pseudo-diffusions and Quadratic term structure models," Papers cond-mat/0212249, arXiv.org, revised Apr 2004.
  3. 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.
  4. MEDDAHI, Nour, 2002. "ARMA Representation of Integrated and Realized Variances," Cahiers de recherche 2002-20, Universite de Montreal, Departement de sciences economiques.
  5. 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, vol. 56(7-8), pages 361-379, July.
  6. Meddahi, N., 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche 2001-26, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  7. 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.
  8. Neil Shephard & Ole E. Barndorff-Nielsen, 2002. "Power Variation and Time Change," Economics Series Working Papers 2002-W24, University of Oxford, Department of Economics.
  9. Di Nunno, Giulia & Sjursen, Steffen, 2014. "BSDEs driven by time-changed Lévy noises and optimal control," Stochastic Processes and their Applications, Elsevier, vol. 124(4), pages 1679-1709.

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