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64
Bayesian Analysis of Stochastic Volatility Models
, 1994
"... this article is to develop new methods for inference and prediction in a simple class of stochastic volatility models in which logarithm of conditional volatility follows an autoregressive (AR) times series model. Unlike the autoregressive conditional heteroscedasticity (ARCH) and gener alized ARCH ..."
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Cited by 371 (21 self)
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this article is to develop new methods for inference and prediction in a simple class of stochastic volatility models in which logarithm of conditional volatility follows an autoregressive (AR) times series model. Unlike the autoregressive conditional heteroscedasticity (ARCH) and gener alized ARCH (GARCH) models [see Bollerslev, Chou, and Kroner (1992) for a survey of ARCH modeling], both the mean and logvolatility equations have separate error terms. The ease of evaluating the ARCH likelihood function and the ability of the ARCH specification to accommodate the timevarying volatility found in many economic time series has fostered an explosion in the use of ARCH models. On the other hand, the likelihood function for stochastic volatility models is difficult to evaluate, and hence these models have had limited empirical application
Stochastic Volatility: Likelihood Inference And Comparison With Arch Models
, 1994
"... this paper we exploit Gibbs sampling to provide a likelihood framework for the analysis of stochastic volatility models, demonstrating how to perform either maximum likelihood or Bayesian estimation. The paper includes an extensive Monte Carlo experiment which compares the efficiency of the maximum ..."
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Cited by 354 (37 self)
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this paper we exploit Gibbs sampling to provide a likelihood framework for the analysis of stochastic volatility models, demonstrating how to perform either maximum likelihood or Bayesian estimation. The paper includes an extensive Monte Carlo experiment which compares the efficiency of the maximum likelihood estimator with that of quasilikelihood and Bayesian estimators proposed in the literature. We also compare the fit of the stochastic volatility model to that of ARCH models using the likelihood criterion to illustrate the flexibility of the framework presented. Some key words: ARCH, Bayes estimation, Gibbs sampler, Heteroscedasticity, Maximum likelihood, Quasimaximum likelihood, Simulation, Stochastic EM algorithm, Stochastic volatility, Stock returns. 1 INTRODUCTION
Estimation of Stochastic Volatility Models with Diagnostics
 Journal of Econometrics
, 1995
"... Efficient Method of Moments (EMM) is used to fit the standard stochastic volatility model and various extensions to several daily financial time series. EMM matches to the score of a model determined by data analysis called the score generator. Discrepancies reveal characteristics of data that stoch ..."
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Cited by 80 (9 self)
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Efficient Method of Moments (EMM) is used to fit the standard stochastic volatility model and various extensions to several daily financial time series. EMM matches to the score of a model determined by data analysis called the score generator. Discrepancies reveal characteristics of data that stochastic volatility models cannot approximate. The two score generators employed here are "Semiparametric ARCH" and "Nonlinear Nonparametric". With the first, the standard model is rejected, although some extensions are accepted. With the second, all versions are rejected. The extensions required for an adequate fit are so elaborate that nonparametric specifications are probably more convenient. Corresponding author: George Tauchen, Duke University, Department of Economics, Social Science Building, Box 90097, Durham NC 277080097 USA, phone 19196601812, FAX 19196848974, email get@tauchen.econ.duke.edu. 0 1 Introduction The stochastic volatility model has been proposed as a descripti...
Estimation of stochastic volatility models via Monte Carlo Maximum Likelihood
, 1998
"... This paper discusses the Monte Carlo maximum likelihood method of estimating stochastic volatility (SV) models. The basic SV model can be expressed as a linear state space model with log chisquare disturbances. The likelihood function can be approximated arbitrarily accurately by decomposing it int ..."
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Cited by 64 (6 self)
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This paper discusses the Monte Carlo maximum likelihood method of estimating stochastic volatility (SV) models. The basic SV model can be expressed as a linear state space model with log chisquare disturbances. The likelihood function can be approximated arbitrarily accurately by decomposing it into a Gaussian part, constructed by the Kalman filter, and a remainder function, whose expectation is evaluated by simulation. No modifications of this estimation procedure are required when the basic SV model is extended in a number of directions likely to arise in applied empirical research. This compares favorably with alternative approaches. The finite sample performance of the new estimator is shown to be comparable to the Monte Carlo Markov chain (MCMC) method.
On the relationship between the conditional mean and volatility of stock returns: A latent VAR approach
, 2002
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Estimating Stochastic Volatility Diffusion Using Conditional Moments of Integrated Volatility
, 2000
"... We exploit the distributional information contained in highfrequency intraday data in constructing a simple conditional moment estimator for stochastic volatility diffusions. The estimator is based on the analytical solutions of the first two conditional moments for the integrated volatility, which ..."
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Cited by 52 (7 self)
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We exploit the distributional information contained in highfrequency intraday data in constructing a simple conditional moment estimator for stochastic volatility diffusions. The estimator is based on the analytical solutions of the first two conditional moments for the integrated volatility, which is effectively approximated by the quadratic variation of the process. We successfully implement the resulting GMM estimator with highfrequency fiveminute foreign exchange and equity index returns. Our simulation evidence and actual empirical results indicate that the method is very reliable and accurate. The computational speed of the procedure compares very favorably to other existing estimation methods in the literature.
Variation, jumps, market frictions and high frequency data in financial econometrics
, 2005
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Maximum likelihood estimation of latent affine processes, Working paper
 Processes, forthcoming, Review of Financial Studies
, 2006
"... This article develops a direct filtrationbased maximum likelihood methodology for estimating the parameters and realizations of latent affine processes. Filtration is conducted in the transform space of characteristic functions, using a version of Bayes β rule for recursively updating the joint cha ..."
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Cited by 24 (1 self)
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This article develops a direct filtrationbased maximum likelihood methodology for estimating the parameters and realizations of latent affine processes. Filtration is conducted in the transform space of characteristic functions, using a version of Bayes β rule for recursively updating the joint characteristic function of latent variables and the data conditional upon past data. An application to daily stock market returns over 195396 reveals substantial divergences from EMMbased estimates; in particular, more substantial and timevarying jump risk. The implications for pricing stock index options are examined. 3 βThe Lion in Affrik and the Bear in Sarmatia are Fierce, but Translated into a Contrary Heaven, are of less Strength and Courage.β Jacob Ziegler; translated by Richard Eden (1555) While models proposing timevarying volatility of asset returns have been around for thirty years, it has proven extraordinarily difficult to estimate the parameters of the underlying volatility process,
MeanReverting Stochastic Volatility
, 2000
"... We present derivative pricing and estimation tools for a class of stochastic volatility models that exploit the observed "bursty" or persistent nature of stock price volatility. An empirical analysis of highfrequency S&P 500 index data confirms that volatility reverts slowly to its mean in comparis ..."
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Cited by 22 (7 self)
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We present derivative pricing and estimation tools for a class of stochastic volatility models that exploit the observed "bursty" or persistent nature of stock price volatility. An empirical analysis of highfrequency S&P 500 index data confirms that volatility reverts slowly to its mean in comparison to the tickbytick fluctuations of the index value, but it is fast meanreverting when looked at over the time scale of a derivative contract (many months). This motivates an asymptotic analysis of the partial differential equation satisfied by derivative prices, utilizing the distinction between these time scales. The analysis yields pricing and implied volatility formulas, and the latter is used to "fit the smile" from European index option prices. The theory identifies the important group parameters that are needed for the derivative pricing and hedging problem for Europeanstyle securities, namely the average volatility and the slope and intercept of the implied volatility line, plotted as a function of the logmoneynesstomaturityratio. The results considerably simplify the estimation procedure, and the data produces estimates