Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns

Harvey, Andrew; Shephard, Neil

doi:10.1080/07350015.1996.10524672

Cited by 286 publications

(310 citation statements)

References 11 publications

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“…The correlation coefficient, enters the parameter vector "( E , , ) over which the likelihood function is optimized. Fitting the model to the CRSP data-set used by Nelson (1991) and Harvey and Shephard (1996) gives the results in Table 8. Not surprisingly, the MCL parameter estimates are not identically equal to the QML estimates reported by Harvey and Shephard (1996).…”

Section: Extensions Of the Basic Sv Model (I»): Non-zero Correlationmentioning

confidence: 99%

“…Fitting the model to the CRSP data-set used by Nelson (1991) and Harvey and Shephard (1996) gives the results in Table 8. Not surprisingly, the MCL parameter estimates are not identically equal to the QML estimates reported by Harvey and Shephard (1996). However, they reflect the general pattern of high volatility persistence and large negative correlation between the return and the (log)variance processes.…”

Section: Extensions Of the Basic Sv Model (I»): Non-zero Correlationmentioning

confidence: 99%

“…Notice, that once the transformation is accomplished, the information regarding the correlation coefficient, is lost, but can be recovered by conditioning on the signs of the original observations (Harvey and Shephard, 1996). Estimation of is addressed in Section 5.4.…”

Section: Stochastic Volatility Modelmentioning

confidence: 99%

“…In the context of QML estimation Harvey and Shephard (1996) shows that this information can be recovered by conditioning on the signs of the returns. The augmented model takes the form:…”

Section: Extensions Of the Basic Sv Model (I»): Non-zero Correlationmentioning

confidence: 99%

“…However, they reflect the general pattern of high volatility persistence and large negative correlation between the return and the (log)variance processes. Both, the likelihood ratio test statistic and the standard Nelson (1991) and Harvey and Shephard (1996). The sample size is ¹"6409 observations.…”

Section: Extensions Of the Basic Sv Model (I»): Non-zero Correlationmentioning

confidence: 99%

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Estimation of stochastic volatility models via Monte Carlo maximum likelihood

Sandmann¹,

Koopman²

1998

Journal of Econometrics

256

215

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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 chi-square 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.1998 Elsevier Science S.A. All rights reserved.JEL classification: C15; C22

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Section: Extensions Of the Basic Sv Model (I»): Non-zero Correlationmentioning

confidence: 99%

Section: Extensions Of the Basic Sv Model (I»): Non-zero Correlationmentioning

confidence: 99%

Section: Stochastic Volatility Modelmentioning

confidence: 99%

“…In the context of QML estimation Harvey and Shephard (1996) shows that this information can be recovered by conditioning on the signs of the returns. The augmented model takes the form:…”

Section: Extensions Of the Basic Sv Model (I»): Non-zero Correlationmentioning

confidence: 99%

Section: Extensions Of the Basic Sv Model (I»): Non-zero Correlationmentioning

confidence: 99%

See 3 more Smart Citations

Estimation of stochastic volatility models via Monte Carlo maximum likelihood

Sandmann¹,

Koopman²

1998

Journal of Econometrics

256

215

View full text Add to dashboard Cite

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A non‐linear filtering approach to stochastic volatility models with an application to daily stock returns

Watanabe

1999

J. Appl. Econ.

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This paper develops a new method for the analysis of stochastic volatility (SV) models. Since volatility is a latent variable in SV models, it is dicult to evaluate the exact likelihood. In this paper, a non-linear ®lter which yields the exact likelihood of SV models is employed. Solving a series of integrals in this ®lter by piecewise linear approximations with randomly chosen nodes produces the likelihood, which is maximized to obtain estimates of the SV parameters. A smoothing algorithm for volatility estimation is also constructed. Monte Carlo experiments show that the method performs well with respect to both parameter estimates and volatility estimates. We illustrate the method by analysing daily stock returns on the Tokyo Stock Exchange. Since the method can be applied to more general models, the SV model is extended so that several characteristics of daily stock returns are allowed, and this more general model is also estimated. have investigated option pricing when volatility changes following a continuous stochastic process such as the Ornstein±Uhlenbeck process, and SV models are discrete approximations to such models.The maximum likelihood method is not easy to implement in SV models, but several alternative methods are now available (Ghysels, et al., 1996, andShephard, 1996 provide good reviews of the

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Stochastic Volatility Models: A Survey with Applications to Option Pricing and Value at Risk

Billio

Sartore

2003

Applied Quantitative Methods for Trading and Investment

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This chapter presents an introduction to the current literature on stochastic volatility models. For these models the volatility depends on some unobserved components or a latent structure.Given the time-varying volatility exhibited by most financial data, in the last two decades there has been a growing interest in time series models of changing variance and the literature on stochastic volatility models has expanded greatly. Clearly, this chapter cannot be exhaustive, however we discuss some of the most important ideas, focusing on the simplest forms of the techniques and models used in the literature.The chapter is organised as follows. Section 1 considers some motivations for stochastic volatility models: empirical stylised facts, pricing of contingent assets and risk evaluation. While section 2 presents models of changing volatility, section 3 focuses on stochastic volatility models and distinguishes between models with continuous and discrete volatility, the latter depending on a hidden Markov chain. Section 4 is devoted to the estimation problem which is still an open question, then a wide range of possibility is given. Sections 5 and 6 introduce some extensions and multivariate models. Finally, in section 7 an estimation program is presented and some possible applications to option pricing and risk evaluation are discussed.Readers interested in the practical utilisation of stochastic volatility models and in the applications can skip section 4.3 without hindering comprehension.

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Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns

Cited by 286 publications

References 11 publications

Estimation of stochastic volatility models via Monte Carlo maximum likelihood

Estimation of stochastic volatility models via Monte Carlo maximum likelihood

A non‐linear filtering approach to stochastic volatility models with an application to daily stock returns

Stochastic Volatility Models: A Survey with Applications to Option Pricing and Value at Risk

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