Markov chain Monte Carlo methods for stochastic volatility models

Chib, Siddhartha; Nardari, Federico; Shephard, Neil

doi:10.1016/s0304-4076(01)00137-3

Cited by 501 publications

(380 citation statements)

References 39 publications

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“…The generalization of the KSC method to Student-t errors was proposed by Chib et al (2002) who also include a generalization of the method for the SV model with jumps.…”

Section: Other Methods Based On Linearizationmentioning

confidence: 99%

Estimation methods for stochastic volatility models: a survey

Broto

Ruiz

2004

Journal of Economic Surveys

191

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The empirical application of Stochastic Volatility (SV) models has been limited due to the difficulties involved in the evaluation of the likelihood function. However, recently there has been fundamental progress in this area due to the proposal of several new estimation methods that try to overcome this problem, being at the same time, empirically feasible. As a consequence, several extensions of the SV models have been proposed and their empirical implementation is increasing. In this paper, we review the main estimators of the parameters and the volatility of univariate SV models proposed in the literature. We describe the main advantages and limitations of each of the methods both from the theoretical and empirical point of view. We complete the survey with an application of the most important procedures to the S&P 500 stock price index.

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“…The generalization of the KSC method to Student-t errors was proposed by Chib et al (2002) who also include a generalization of the method for the SV model with jumps.…”

Section: Other Methods Based On Linearizationmentioning

confidence: 99%

Estimation methods for stochastic volatility models: a survey

Broto

Ruiz

2004

Journal of Economic Surveys

191

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“…As we have mentioned, in addition to integrating out parameter uncertainty, the marginal likelihood of stochastic volatility models also integrates out the uncertainty associated with the latent volatilities. In the past, particle filters have been applied to stochastic volatility models to integrate out volatility (see Chib et al (2002)). …”

Section: Predictabilitymentioning

confidence: 99%

Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture

Jensen

Maheu

2012

SSRN Journal

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In this paper, we extend the parametric, asymmetric, stochastic volatility model (ASV), where returns are correlated with volatility, by flexibly modeling the bivariate distribution of the return and volatility innovations nonparametrically. Its novelty is in modeling the joint, conditional, return-volatility distribution with an infinite mixture of bivariate Normal distributions with mean zero vectors, but having unknown mixture weights and covariance matrices. This semiparametric ASV model nests stochastic volatility models whose innovations are distributed as either Normal or Student-t distributions, plus the response in volatility to unexpected return shocks is more general than the fixed asymmetric response with the ASV model. The unknown mixture parameters are modeled with a Dirichlet process prior. This prior ensures a parsimonious, finite, posterior mixture that best represents the distribution of the innovations and a straightforward sampler of the conditional posteriors. We develop a Bayesian Markov chain Monte Carlo sampler to fully characterize the parametric and distributional uncertainty. Nested model comparisons and out-ofsample predictions with the cumulative marginal-likelihoods, and one-day-ahead, predictive logBayes factors between the semiparametric and parametric versions of the ASV model shows the semiparametric model projecting more accurate empirical market returns. A major reason is how volatility responds to an unexpected market movement. When the market is tranquil, expected volatility reacts to a negative (positive) price shock by rising (initially declining, but then rising when the positive shock is large). However, when the market is volatile, the degree of asymmetry and the size of the response in expected volatility is muted. In other words, when times are good, no news is good news, but when times are bad, neither good nor bad news matters with regards to volatility. JEL classification: C11, C14, C53, C58

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“…s t q t can be viewed as a discretization of a finite activity Lévy process. This model was introduced in Chib et al (2002) and Berg et al (2004). The estimation of φ is complicated by the fact that volatility and jump components are both latent.…”

Section: Unit Root Test In a Stochastic Volatility Model With Jumpsmentioning

confidence: 99%

Bayesian hypothesis testing in latent variable models

Yong

2012

Journal of Econometrics

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Hypothesis testing using Bayes factors (BFs) is known not to be well defined under the improper prior. In the context of latent variable models, an additional problem with BFs is that they are difficult to compute. In this paper, a new Bayesian method, based on decision theory and the EM algorithm, is introduced to test a point hypothesis in latent variable models. The new statistic is a by-product of the Bayesian MCMC output and, hence, easy to compute. It is shown that the new statistic is easy to interpret and appropriately defined under improper priors because the method employs a continuous loss function. The method is illustrated using a one-factor asset pricing model and a stochastic volatility model with jumps.JEL classification: C11, C12, G12.

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Markov chain Monte Carlo methods for stochastic volatility models

Cited by 501 publications

References 39 publications

Estimation methods for stochastic volatility models: a survey

Estimation methods for stochastic volatility models: a survey

Estimating a Semiparametric Asymmetric Stochastic Volatility Model with a Dirichlet Process Mixture

Bayesian hypothesis testing in latent variable models

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