Statistical aspects of ARCH and stochastic volatility

Shephard, Neil

doi:10.1007/978-1-4899-2879-5_1

Cited by 455 publications

(437 citation statements)

References 108 publications

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“…Alternatively, volatility may be modelled as an unobserved component following some latent stochastic process, such as an autoregression. Models of this kind are known as stochastic volatility (SV) models (Taylor, 1994;Ghysels et al, 1996;Shephard, 1996).…”

Section: Introductionmentioning

confidence: 99%

Estimation of stochastic volatility models via Monte Carlo maximum likelihood

Sandmann¹,

Koopman²

1998

Journal of Econometrics

254

211

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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: Introductionmentioning

confidence: 99%

Estimation of stochastic volatility models via Monte Carlo maximum likelihood

Sandmann¹,

Koopman²

1998

Journal of Econometrics

254

211

View full text Add to dashboard Cite

show abstract

“…As noted in McAleer et al (2007), there are some important differences between EGARCH and the previous two models, as follows: (i) EGARCH is a model of the logarithm of the conditional variance, which implies that no restrictions on the parameters are required to ensure 0  t h ; (ii) moment conditions are required for the GARCH and GJR models as they are dependent on lagged unconditional shocks, whereas EGARCH does not require moment conditions to be established as it depends on lagged conditional shocks (or standardized residuals); (iii) Shephard (1996) observed that 1 | |   is likely to be a sufficient condition for consistency of QMLE for EGARCH(1,1); (iv) as the standardized residuals appear in equation (7), 1 | |   would seem to be a sufficient condition for the existence of moments; and (v) in addition to being a sufficient condition for consistency,…”

Section: Egarchmentioning

confidence: 99%

Risk management of risk under the Basel Accord: A Bayesian approach to forecasting Value-at-Risk of VIX futures

Casarin

Chang

Jiménez-Martín

et al. 2013

Mathematics and Computers in Simulation

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It is well known that the Basel II Accord requires banks and other Authorized Deposit-taking Institutions (ADIs) to communicate their daily risk forecasts to the appropriate monetary authorities at the beginning of each trading day, using one or more risk models, whether individually or as combinations, to measure Value-at-Risk (VaR). The risk estimates of these models are used to determine capital requirements and associated capital costs of ADIs, depending in part on the number of previous violations, whereby realised losses exceed the estimated VaR. Previous papers proposed a new approach to model selection for predicting VaR, consisting of combining alternative risk models, and comparing conservative and aggressive strategies for choosing between VaR models. This paper, using Bayesian and non-Bayesian combinations of models addresses the question of risk management of risk, namely VaR of VIX futures prices, and extends the approaches given in previous papers to examine how different risk management strategies performed during the 2008–2009 global financial crisis (GFC). The use of time-varying weights using Bayesian methods, allows dynamic combinations of the different models to obtain a more accurate VaR forecasts than the estimates and forecasts that might be produced by a single model of risk. One of these dynamic combinations is endogenously determined by the pass performance in terms of daily capital charges of the individual models. This can improve the strategies to minimize daily capital charges, which is a central objective of ADIs. The empirical results suggest that an aggressive strategy of choosing the Supremum of single model forecasts, as compared with Bayesian and non-Bayesian combinations of models, is preferred to other alternatives, and is robust during the GFC

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“…By introducing a temporal dimension to the selection of the importance function, an adaptive perspective can be achieved at little cost, for a potentially large gain in efficiency. Celeux et al (2003) have shown that the PMC scheme is a viable alternative to MCMC schemes in missing data settings, among others for the stochastic volatility model (Shephard 1996). Even with the standard choice of the full conditional distributions, this method provides an accurate representation of the distribution of interest in a few iterations.…”

Section: Population Monte Carlo Approximationsmentioning

confidence: 99%

Bayesian Modelling and Inference on Mixtures of Distributions

Marin¹,

Mengersen²,

Robert³

2005

Handbook of Statistics

322

361

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'But, as you have already pointed out, we do not need any more disjointed clues,' said Bartholomew. 'That has been our problem all along: we have a mass of small facts and small scraps of information, but we are unable to make any sense out of them. The last thing we need is more.' Susanna Gregory, A Summer of Discontent IntroductionToday's data analysts and modellers are in the luxurious position of being able to more closely describe, estimate, predict and infer about complex systems of interest, thanks to ever more powerful computational methods but also wider ranges of modelling distributions. Mixture models constitute a fascinating illustration of these aspects: while within a parametric family, they offer malleable approximations in non-parametric settings; although based on standard distributions, they pose highly complex computational challenges; and they are both easy to constrain to meet identifiability requirements and fall within the class of ill-posed problems. They also provide an endless benchmark for assessing new techniques, from the EM algorithm to reversible jump methodology. In particular, they exemplify the

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Statistical aspects of ARCH and stochastic volatility

Cited by 455 publications

References 108 publications

Estimation of stochastic volatility models via Monte Carlo maximum likelihood

Estimation of stochastic volatility models via Monte Carlo maximum likelihood

Risk management of risk under the Basel Accord: A Bayesian approach to forecasting Value-at-Risk of VIX futures

Bayesian Modelling and Inference on Mixtures of Distributions

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