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Analysis of filtering and smoothing algorithms for Lévy-driven stochastic volatility models

  • Creal, Drew D.

Filtering and smoothing algorithms that estimate the integrated variance in Lévy-driven stochastic volatility models are analyzed. Particle filters are algorithms designed for nonlinear, non-Gaussian models while the Kalman filter remains the best linear predictor if the model is linear but non-Gaussian. Monte Carlo experiments are performed to compare these algorithms across different specifications of the model including different marginal distributions and degrees of persistence for the instantaneous variance. The use of realized variance as an observed variable in the state space model is also evaluated. Finally, the particle filter's ability to identify the timing and size of jumps is assessed relative to popular nonparametric estimators.

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File URL: http://www.sciencedirect.com/science/article/B6V8V-4P8SJ5J-2/1/8e3b2bc43f9165059ad888b155dccc8d
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Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 52 (2008)
Issue (Month): 6 (February)
Pages: 2863-2876

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Handle: RePEc:eee:csdana:v:52:y:2008:i:6:p:2863-2876
Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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  1. 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.
  2. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382.
  3. Ole E. Barndorff-Nielsen, 2003. "Integrated OU Processes and Non-Gaussian OU-based Stochastic Volatility Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(2), pages 277-295.
  4. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
  5. Elisa Nicolato & Emmanouil Venardos, 2003. "Option Pricing in Stochastic Volatility Models of the Ornstein-Uhlenbeck type," Mathematical Finance, Wiley Blackwell, vol. 13(4), pages 445-466.
  6. Henghsiu Tsai & K. S. Chan, 2005. "A note on non-negative continuous time processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 589-597.
  7. Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Impact of jumps on returns and realised variances: econometric analysis of time-deformed Levy processes," Economics Papers 2003-W12, Economics Group, Nuffield College, University of Oxford.
  8. 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.
  9. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 1-37.
  10. Raggi, Davide & Bordignon, Silvano, 2006. "Comparing stochastic volatility models through Monte Carlo simulations," Computational Statistics & Data Analysis, Elsevier, vol. 50(7), pages 1678-1699, April.
  11. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543, March.
  12. 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.
  13. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Normal modified stable processes," Economics Papers 2001-W6, Economics Group, Nuffield College, University of Oxford.
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