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Bayesian inference with stochastic volatility models using continuous superpositions of non-Gaussian Ornstein-Uhlenbeck processes

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  • Griffin, Jim
  • Steel, Mark F.J.

Abstract

This paper discusses Bayesian inference for stochastic volatility models based on continuous superpositions of Ornstein-Uhlenbeck processes. These processes represent an alternative to the previously considered discrete superpositions. An interesting class of continuous superpositions is defined by a Gamma mixing distribution which can define long memory processes. We develop efficient Markov chain Monte Carlo methods which allow the estimation of such models with leverage effects. This model is compared with a two-component superposition on the daily Standard and Poor's 500 index from 1980 to 2000.

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File URL: http://mpra.ub.uni-muenchen.de/11071/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 11071.

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Date of creation: 13 Oct 2008
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Handle: RePEc:pra:mprapa:11071

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Keywords: Leverage effect; Levy process; Long memory; Markov chain Monte Carlo; Stock price;

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  1. Creal, Drew D., 2008. "Analysis of filtering and smoothing algorithms for Lévy-driven stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2863-2876, February.
  2. Josep Perello & Jaume Masoliver & Jean-Philippe Bouchaud, 2004. "Multiple time scales in volatility and leverage correlations: a stochastic volatility model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 11(1), pages 27-50.
  3. Griffin, J.E. & Steel, M.F.J., 2006. "Inference with non-Gaussian Ornstein-Uhlenbeck processes for stochastic volatility," Journal of Econometrics, Elsevier, vol. 134(2), pages 605-644, October.
  4. S. P. Brooks & P. Giudici & G. O. Roberts, 2003. "Efficient construction of reversible jump Markov chain Monte Carlo proposal distributions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 3-39.
  5. 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.
  6. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, 06.
  7. Sylvia Frühwirth-Schnatter & Leopold Sögner, 2009. "Bayesian estimation of stochastic volatility models based on OU processes with marginal Gamma law," Annals of the Institute of Statistical Mathematics, Springer, vol. 61(1), pages 159-179, March.
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Cited by:
  1. Raknerud, Arvid & Skare, Øivind, 2012. "Indirect inference methods for stochastic volatility models based on non-Gaussian Ornstein–Uhlenbeck processes," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3260-3275.

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