Markov chain Monte Carlo and data augmentation methods for continuous-time stochastic volatility models

Persistent Link:
http://hdl.handle.net/10150/283976
Title:
Markov chain Monte Carlo and data augmentation methods for continuous-time stochastic volatility models
Author:
Witte, Hugh Douglas
Issue Date:
1999
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
In this paper we exploit some recent computational advances in Bayesian inference, coupled with data augmentation methods, to estimate and test continuous-time stochastic volatility models. We augment the observable data with a latent volatility process which governs the evolution of the data's volatility. The level of the latent process is estimated at finer increments than the data are observed in order to derive a consistent estimator of the variance over each time period the data are measured. The latent process follows a law of motion which has either a known transition density or an approximation to the transition density that is an explicit function of the parameters characterizing the stochastic differential equation. We analyze several models which differ with respect to both their drift and diffusion components. Our results suggest that for two size-based portfolios of U.S. common stocks, a model in which the volatility process is characterized by nonstationarity and constant elasticity of instantaneous variance (with respect to the level of the process) greater than 1 best describes the data. We show how to estimate the various models, undertake the model selection exercise, update posterior distributions of parameters and functions of interest in real time, and calculate smoothed estimates of within sample volatility and prediction of out-of-sample returns and volatility. One nice aspect of our approach is that no transformations of the data or the latent processes, such as subtracting out the mean return prior to estimation, or formulating the model in terms of the natural logarithm of volatility, are required.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Statistics.; Economics, Finance.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Business Administration
Degree Grantor:
University of Arizona
Advisor:
Lamoureux, Christopher G.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleMarkov chain Monte Carlo and data augmentation methods for continuous-time stochastic volatility modelsen_US
dc.creatorWitte, Hugh Douglasen_US
dc.contributor.authorWitte, Hugh Douglasen_US
dc.date.issued1999en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractIn this paper we exploit some recent computational advances in Bayesian inference, coupled with data augmentation methods, to estimate and test continuous-time stochastic volatility models. We augment the observable data with a latent volatility process which governs the evolution of the data's volatility. The level of the latent process is estimated at finer increments than the data are observed in order to derive a consistent estimator of the variance over each time period the data are measured. The latent process follows a law of motion which has either a known transition density or an approximation to the transition density that is an explicit function of the parameters characterizing the stochastic differential equation. We analyze several models which differ with respect to both their drift and diffusion components. Our results suggest that for two size-based portfolios of U.S. common stocks, a model in which the volatility process is characterized by nonstationarity and constant elasticity of instantaneous variance (with respect to the level of the process) greater than 1 best describes the data. We show how to estimate the various models, undertake the model selection exercise, update posterior distributions of parameters and functions of interest in real time, and calculate smoothed estimates of within sample volatility and prediction of out-of-sample returns and volatility. One nice aspect of our approach is that no transformations of the data or the latent processes, such as subtracting out the mean return prior to estimation, or formulating the model in terms of the natural logarithm of volatility, are required.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectStatistics.en_US
dc.subjectEconomics, Finance.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineBusiness Administrationen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorLamoureux, Christopher G.en_US
dc.identifier.proquest9946855en_US
dc.identifier.bibrecord.b39918166en_US
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