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Inference With Non-Gaussian Ornstein-Uhlenbeck Processes for Stochastic Volatility

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Author Info
James E. Griffin (University of Kent at Canterbury)
Mark F.J. Steel (University of Kent at Canterbury)

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Abstract

Continuous-time stochastic volatility models are becoming a more and more popular way to describe moderate and high-frequency financial data. Recently, Barndorff-Nielsen and Shephard (2001a) proposed a class of models where the volatility behaves according to an Ornstein-Uhlenbeck process, driven by a positive Levy process without Gaussian component. They also consider superpositions of such processes and we extend that to the inclusion of an uncorrelated component. Our aim is to design and implement practically relevant inference methods for such models, within the Bayesian paradigm. The algorithm is based on Markov chain Monte Carlo methods and we use a series representation of Levy processes. Inference for such models is complicated by the fact that parameter changes will often induce a change of dimension in the representation of the process and the associated problem of overconditioning. We avoid this problem by dependent thinning methods. An application to stock price data shows the models perform very well, even in the face of data with rapid changes, especially if a superposition of processes is used. After introducing some extra flexibility, the model can even be used to describe spot interest rate data with considerable success.

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Paper provided by EconWPA in its series Econometrics with number 0201002.

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Length: 33 pages
Date of creation: 06 Jan 2002
Date of revision: 04 Apr 2003
Handle: RePEc:wpa:wuwpem:0201002

Note: Type of Document - LaTeX; prepared on IBM PC - PC-TEX; to print on HP/PostScript (A4); pages: 33 ; figures: included
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Related research
Keywords: Bayesian methods; Deposit spot rate; Levy process; Markov chain Monte Carlo; Stock price;

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Find related papers by JEL classification:
C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Bayesian Analysis
G0 - Financial Economics - - General

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References listed on IDEAS
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    Other versions:
  3. Suresh M. Sundaresan, 2000. "Continuous-Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, 08. [Downloadable!] (restricted)
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    Other versions:
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    Other versions:
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Griffin, Jim & Steel, Mark F.J., 2008. "Bayesian inference with stochastic volatility models using continuous superpositions of non-Gaussian Ornstein-Uhlenbeck processes," MPRA Paper 11071, University Library of Munich, Germany. [Downloadable!]
  2. Friedrich Hubalek & Petra Posedel, 2008. "Joint analysis and estimation of stock prices and trading volume in Barndorff-Nielsen and Shephard stochastic volatility models," Quantitative Finance Papers 0807.3464, arXiv.org, revised Oct 2008. [Downloadable!]
  3. Almut E. D. Veraart, 2008. "Impact of time–inhomogeneous jumps and leverage type effects on returns and realised variances," CREATES Research Papers 2008-57, School of Economics and Management, University of Aarhus. [Downloadable!]
  4. Emanuele Taufer, 2008. "Characteristic function estimation of non-Gaussian Ornstein-Uhlenbeck processes," DISA Working Papers 0805, Department of Computer and Management Sciences, University of Trento, Italy, revised 07 Jul 2008. [Downloadable!]
  5. 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. [Downloadable!] (restricted)
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