Griffin, Jim and Steel, Mark F.J. (2008): Bayesian inference with stochastic volatility models using continuous superpositions of non-Gaussian Ornstein-Uhlenbeck processes.
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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.
|Item Type:||MPRA Paper|
|Original Title:||Bayesian inference with stochastic volatility models using continuous superpositions of non-Gaussian Ornstein-Uhlenbeck processes|
|Keywords:||Leverage effect; Levy process; Long memory; Markov chain Monte Carlo; Stock price|
|Subjects:||C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models; Multiple Variables > C32 - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
G - Financial Economics > G1 - General Financial Markets > G10 - General
C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General
|Depositing User:||Mark F.J. Steel|
|Date Deposited:||14. Oct 2008 05:04|
|Last Modified:||16. Feb 2013 03:20|
Barndorff-Nielsen, O. E. (2001): “Superposition of Ornstein-Uhlenbeck type processes,” Theory of Probability and its Applications, 45, 175-194.
Barndorff-Nielsen, O. E. and N. Shephard (2001): “Non-Gaussian OU based models and some of their uses in financial economics,” Journal of the Royal Statistical Society B, 63, 167-241 (with discussion).
Black, F. (1976): “Studies of stock price volatility changes,” Proc. Bus. Statist. Sect. Am. Statist. Ass., 177-181.
Bondesson, L. (1988): “Shot-Noise Processes and Distributions,” Encyclopedia of Statistical Science, Vol 8. Wiley: New York.
Brooks, S. P., P. Giudici and G. O. Roberts (2003): “Efficient construction of reversible jump Markov chain Monte Carlo proposal distributions,” Journal of the Royal Statistical Society B, 65, 3-55.
Carpenter, J., P. Clifford and P. Fearnhead (1999): “An improved particle filter for non-linear problems,” IEE proceedings - Radar, Sonar and Navigation, 146, 2-7.
Creal, D. D. (2008): “Analysis of filtering and smoothing algorithms for L´evydriven stochastic volatility models,” Computational Statistics and Data Analysis, 52, 2863-2876.
Devroye, L. (1986): “Non-Uniform Random Variate Generation,” Springer- Verlag: New York.
Ferguson, T. and Klass, M. J. (1972): “A representation of independent increment processes without Gaussian components. Annals of Mathematical Statistics, 43, 1634-1643.
Fruehwirth-Schnatter, S. and L. Soegner (2008): “Bayesian Estimation of Stochastic Volatility Models based onOUprocesses with Marginal Gamma Law,” The Annals of the Institute of Statistical Mathematics, forthcoming.
Gander, M. P. S. and D. A. Stephens (2007a): “Stochastic Volatility Modelling with General Marginal Distributions: Inference, Prediction and Model Selection,” Journal of Statistical Planning and Inference, 137, 3068-3081.
Gander, M. P. S. and D. A. Stephens (2007b): “Simulation and inference for stochastic volatility models driven by L´evy processes,” Biometrika, 94, 627-646.
Green, P. J. (1995): “Reversible jump Markov chain Monte Carlo computation and Bayesian model determination,” Biometrika, 82, 711-732.
Griffin, J. E. and M. F. J. Steel (2006): “Inference with non-Gaussian Ornstein- Uhlenbeck processes for stochastic volatility,” Journal of Econometrics, 134, 605-644.
Li, H., M. T.Wells and C. Yu (2008): “A Bayesian analysis of returns dynamics with L´evy jumps,” Review of Financial Studies, 21, 2345 - 2378.
Newton, M. A. and A. E. Raftery (1994): “Approximate Bayesian inference by the weighted likelihood bootstrap,” Journal of the Royal Statistical Society B, 56, 3-48.
Nicolato, E. and E. Venardos (2003): “Option pricing in stochastic volatility models of the Ornstein-Uhlenbeck type,” Mathematical Finance, 13, 445- 466.
Roberts, G. O., O. Papaspiliopoulos and P. Dellaportas (2004): “Bayesian inference for non-Gaussian Ornstein-Uhlenbeck stochastic volatility processes,” Journal of the Royal Statistical Society B, 66, 369-393.
Rosinski, J. (2001): “Series representations of L´evy processes from the perspective of point process,” in L´evy processes - Theory and Applications eds.: O. E. Barndorff-Nielsen, T. Mikosch and S. Resnick. Birkhauser: Boston.