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Using stochastic volatility models to analyse weekly ozone averages in Mexico City

ACHCAR, Jorge A.; RODRIGUES, Eliane R.; TZINTZUN, Guadalupe
Fonte: SPRINGER; AMSTERDAM Publicador: SPRINGER; AMSTERDAM
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
66.43%
In this paper we make use of some stochastic volatility models to analyse the behaviour of a weekly ozone average measurements series. The models considered here have been used previously in problems related to financial time series. Two models are considered and their parameters are estimated using a Bayesian approach based on Markov chain Monte Carlo (MCMC) methods. Both models are applied to the data provided by the monitoring network of the Metropolitan Area of Mexico City. The selection of the best model for that specific data set is performed using the Deviance Information Criterion and the Conditional Predictive Ordinate method.; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); CNPq Conselho Nacional de Pesquisa-Brazil[300235/2005-4]; Direccion General de Apoyo al Personal Academico of the Universidad Nacional Autonoma de Mexico[968SFA/2007]; Direccion General de Apoyo al Personal Academico of the Universidad Nacional Autonoma de Mexico; Department of Statistics at the University of Oxford; Department of Statistics at the University of Oxford

Stochastic volatility model with filtering

Elliott, R.; Miao, H.
Fonte: Marcel Dekker Inc Publicador: Marcel Dekker Inc
Tipo: Artigo de Revista Científica
Publicado em //2006 EN
Relevância na Pesquisa
66.49%
We generalize the stochastic volatility model by allowing the volatility to follow different dynamics in different states of the world. The dynamics of the "states of the world" are represented by a Markov chain. We estimate all the parameters by using the filtering and the EM algorithms. Closed form estimates for all parameters are derived in this paper. These estimates can be updated using new information as it arrives.; Robert J. Elliott; Hong Miao; Copyright © Taylor & Francis Group, LLC

Filtering a nonlinear stochastic volatility model

Elliott, R.; Siu, T.; Fung, E.
Fonte: Kluwer Academic Publ Publicador: Kluwer Academic Publ
Tipo: Artigo de Revista Científica
Publicado em //2012 EN
Relevância na Pesquisa
66.56%
We introduce a class of stochastic volatility models whose parameters are modulated by a hidden nonlinear dynamical system. Our aim is to incorporate the impact of economic cycles, or business cycles, into the long-term behavior of volatility dynamics. We develop a discrete-time nonlinear filter for the estimation of the hidden volatility and the nonlinear dynamical system based on return observations. By exploiting the technique of a reference probability measure we derive filters for the hidden volatility and the nonlinear dynamical system.; Robert J. Elliott, Tak Kuen Siu and Eric S. Fung

Common Drifting Volatility in Large Bayesian VARs

CARRIERO, Andrea; CLARK, Todd E.; MARCELLINO, Massimiliano
Fonte: Instituto Universitário Europeu Publicador: Instituto Universitário Europeu
Tipo: Trabalho em Andamento Formato: application/pdf; digital
EN
Relevância na Pesquisa
56.7%
The estimation of large Vector Autoregressions with stochastic volatility using standard methods is computationally very demanding. In this paper we propose to model conditional volatilities as driven by a single common unobserved factor. This is justified by the observation that the pattern of estimated volatilities in empirical analyses is often very similar across variables. Using a combination of a standard natural conjugate prior for the VAR coefficients, and an independent prior on a common stochastic volatility factor, we derive the posterior densities for the parameters of the resulting BVAR with common stochastic volatility (BVAR-CSV). Under the chosen prior the conditional posterior of the VAR coefficients features a Kroneker structure that allows for fast estimation, even in a large system. Using US and UK data, we show that, compared to a model with constant volatilities, our proposed common volatility model significantly improves model fit and forecast accuracy. The gains are comparable to or as great as the gains achieved with a conventional stochastic volatility specification that allows independent volatility processes for each variable. But our common volatility specification greatly speeds computations.

Volatility modelling and accurate minimun capital risk requirements : a comparison among several approaches

Grané, Aurea; Veiga, Helena
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: Trabalho em Andamento Formato: application/pdf
Publicado em /05/2007 ENG; ENG
Relevância na Pesquisa
56.59%
In this paper we estimate, for several investment horizons, minimum capital risk requirements for short and long positions, using the unconditional distribution of three daily indexes futures returns and a set of GARCH-type and stochastic volatility models. We consider the possibility that errors follow a t-Student distribution in order to capture the kurtosis of the returns distributions. The results suggest that an accurate modeling of extreme returns obtained for long and short trading investment positions is possible with a simple autoregressive stochastic volatility model. Moreover, modeling volatility as a fractional integrated process produces, in general, excessive volatility persistence and consequently leads to large minimum capital risk requirement estimates. The performance of models is assessed with the help of out-of-sample tests and p-values of them are reported.

Quasi-Maximum Likelihood estimation of Stochastic Volatility models

Ruiz, Esther
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica Formato: application/pdf
Publicado em //1994 ENG
Relevância na Pesquisa
66.58%
Changes in variance or volatility over time can be modelled using stochastic volatility (SV) models. This approach is based on treating the volatility as an unobserved vatiable, the logarithm of which is modelled as a linear stochastic process, usually an autoregression. This article analyses the asymptotic and finite sample properties of a Quasi-Maximum Likelihood (QML) estimator based on the Kalman filter. The relative efficiency of the QML estimator when compared with estimators based on the Generalized Method of Moments is shown to be quite high for parameter values often found in empirical applications. The QML estimator can still be employed when the SV model is generalized to allow for distributions with heavier tails than the normal. SV models are finally fitted to daily observations on the yen/dollar exchange rate.; Publicado además en: Recent developments in Time Series, 2003, vol. 2, ISBN13: 9781840649512, pp. 117-134

Stochastic volatility versus autoregressive conditional heteroscedasticity

Ruiz, Esther
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: Trabalho em Andamento Formato: application/pdf
Publicado em /12/1993 ENG
Relevância na Pesquisa
66.53%
During the last few years there has been an increasing interest in modelling time-varying volatilities of high frequency financial time series. Several models have been proposed, being the most popular between econometricians the autoregressive conditional heteroscedasticity (ARCH) based models. However, in the financial literature stochastic volatility (SV) models have been widely used, mainly when dealing with option valuation models. Both kinds of models imply similar statistical properties on the returns series and both are able of explaining the stilized facts often observed in empirical time series of returns (high kurtosis, autocorrelations of the squares etc;). It is of interest to apply each of these alternative models to the same data set, with the aim of investigating the different implications each might have for the predictability of volatility. In particular, we consider three models, GARCH(l,l), EGARCH(l,l) and AR(l)-SV, and fit each of them to four daily exchange rates. Comparisons are made between the corresponding univariate models. The main conclusion is that there are important differences between the models in the one-step-ahead predictions of volatility. SV models fit better in the center of the distribution of returns while GARCH and EGARCH models are better in the tails of the distribution.

Forecasting volatility: does continuous time do better than discrete time?

Bretó, Carles; Veiga, Helena
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: info:eu-repo/semantics/draft; info:eu-repo/semantics/workingPaper Formato: application/pdf
Publicado em /07/2011 ENG
Relevância na Pesquisa
56.71%
In this paper we compare the forecast performance of continuous and discrete-time volatility models. In discrete time, we consider more than ten GARCH-type models and an asymmetric autoregressive stochastic volatility model. In continuous-time, a stochastic volatility model with mean reversion, volatility feedback and leverage. We estimate each model by maximum likelihood and evaluate their ability to forecast the two scales realized volatility, a nonparametric estimate of volatility based on highfrequency data that minimizes the biases present in realized volatility caused by microstructure errors. We find that volatility forecasts based on continuous-time models may outperform those of GARCH-type discrete-time models so that, besides other merits of continuous-time models, they may be used as a tool for generating reasonable volatility forecasts. However, within the stochastic volatility family, we do not find such evidence. We show that volatility feedback may have serious drawbacks in terms of forecasting and that an asymmetric disturbance distribution (possibly with heavy tails) might improve forecasting.

Comentario sobre “Bayesian Analysis of Stochastic Volatility models”

Harvey, Andrew; Ruiz, Esther
Fonte: JSTOR Publicador: JSTOR
Tipo: info:eu-repo/semantics/acceptedVersion; info:eu-repo/semantics/article Formato: text/plain; application/pdf
Publicado em //1994 ENG
Relevância na Pesquisa
66.43%
There has been an increasing interest in stochastic volatility (SV) models in the last two or three years. Such models are appealing because they follow very naturally from much of finance theory and their properties are relatively easy to derive. Nevertheless, most econometric work has been carried out within the autoregressive conditional heteroscedasticity (ARCH) framework. By assuming that conditional variance is an exact function of past observations, ARCH models are formulated in such a way that the likelihood function may be obtained directly. SV models do not have this property, and this article by Jacquier, Polson, and Rossi (JPR) is an important contribution in that it provides a relatively efficient method of estimation.

One for all : nesting asymmetric stochastic volatility models

Mao, Xiuping; Ruiz, Esther; Veiga, Helena
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: info:eu-repo/semantics/draft; info:eu-repo/semantics/workingPaper Formato: application/pdf; text/plain
Publicado em /05/2013 ENG
Relevância na Pesquisa
66.57%
This paper proposes a new stochastic volatility model to represent the dynamic evolution of conditionally heteroscedastic time series with leverage effect. Although there are already several models proposed in the literature with the same purpose, our main justification for a further new model is that it nests some of the most popular stochastic volatility specifications usually implemented to real time series of financial returns. We derive closed-form expressions of its statistical properties and, consequently, of those of the nested specifications. Some of these properties were previously unknown in the literature although the restricted models are often fitted by empirical researchers. By comparing the properties of the restricted models, we are able to establish the advantages and limitations of each of them. Finally, we analyze the performance of a MCMC estimator of the parameters and volatilities of the new proposed model and show that, if the error distribution is known, it has appropriate finite sample properties. Furthermore, estimating the new model using the MCMC estimator, one can correctly identify the restricted true specifications. All the results are illustrated by estimating the parameters and volatilities of simulated time series and of a series of daily S&P500 returns; Financial support from the Spanish Ministry of Education and Science...

Particle learning for Bayesian non-parametric Markov Switching Stochastic Volatility model

Virbickaite, Audrone; Lopes, Hedibert F.; Ausín, Concepcion; Galeano, Pedro
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: info:eu-repo/semantics/draft; info:eu-repo/semantics/workingPaper
Publicado em /10/2014 ENG
Relevância na Pesquisa
66.43%
This paper designs a Particle Learning (PL) algorithm for estimation of Bayesian nonparametric Stochastic Volatility (SV) models for financial data. The performance of this particle method is then compared with the standard Markov Chain Monte Carlo (MCMC) methods for non-parametric SV models. PL performs as well as MCMC, and at the same time allows for on-line type inference. The posterior distributions are updated as new data is observed, which is prohibitively costly using MCMC. Further, a new non-parametric SV model is proposed that incorporates Markov switching jumps.The proposed model is estimated by using PL and tested on simulated data. Finally, the performance of the two non-parametric SV models, with and without Markov switching, is compared by using real financial time series. The results show that including a Markov switching specification provides higher predictive power in the tails of the distribution.; Virbickaite, A. and Ausín, C.M. are grateful for the financial support from MEC grant ECO2011-25706. Galeano, P. acknowledges financial support from MEC grant ECO2012- 38442

Score driven asymmetric stochastic volatility models

Mao, Xiuping; Ruiz, Esther; Veiga, Helena
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: info:eu-repo/semantics/draft; info:eu-repo/semantics/workingPaper
Publicado em /10/2014 ENG
Relevância na Pesquisa
66.53%
In this paper we propose a new class of asymmetric stochastic volatility (SV) models, which specifies the volatility as a function of the score of the distribution of returns conditional on volatilities based on the Generalized Autoregressive Score (GAS) model. Different specifications of the log-volatility are obtained by assuming different return error distributions. In particular, we consider three of the most popular distributions, namely, the Normal, Student-t and Generalized Error Distribution and derive the statistical properties of each of the corresponding score driven SV models. We show that some of the parameters cannot be property identified by the moments usually considered as to describe the stylized facts of financial returns, namely, excess kurtosis, autocorrelations of squares and cross-correlations between returns and future squared returns. The parameters of some restricted score driven SV models can be estimated adequately using a MCMC procedure. Finally, the new proposed models are fitted to financial returns and evaluated in terms of their in-sample and out-of-sample performance; Financial support from the Spanish Ministry of Education and Science, research project ECO2012-32401, is acknowledged. The third author is also grateful for project MTM2010-17323

Pricing variance and volatility swaps in a stochastic volatility model with regime switching: discrete observations case

Elliott, R.; Lian, G.
Fonte: IOP Publishing Ltd. Publicador: IOP Publishing Ltd.
Tipo: Artigo de Revista Científica
Publicado em //2013 EN
Relevância na Pesquisa
66.6%
This study presents a set of closed-form exact solutions for pricing discretely sampled variance swaps and volatility swaps, based on the Heston stochastic volatility model with regime switching. In comparison with all the previous studies in the literature, this research, which obtains closed-form exact solutions for variance and volatility swaps with discrete sampling times, serves several purposes. (1) It verifies the degree of validity of Elliott et al.'s [Appl. Math. Finance, 2007, 14(1), 41–62] continuous-sampling-time approximation for variance and volatility swaps of relatively short sampling periods. (2) It examines the effect of ignoring regime switching on pricing variance and volatility swaps. (3) It contributes to bridging the gap between Zhu and Lian's [Math. Finance, 2011, 21(2), 233–256] approach and Elliott et al.'s framework. (4) Finally, it presents a semi-Monte-Carlo simulation for the pricing of other important realized variance based derivatives.; Robert J. Elliott and Guang-Hua Lian

NEW TOOLS FOR VOLATILITY MODELS

SANTILLI, MANOLA
Fonte: La Sapienza Universidade de Roma Publicador: La Sapienza Universidade de Roma
Tipo: Tese de Doutorado
EN
Relevância na Pesquisa
56.67%
In the first part of this work, we propose a new estimation method of the spot volatility, based on a semi-nonparametric model, which employs the information content of a complete panel of European options, daily quoted in the market, under no arbitrage assumptions. The technique we propose is based on the idea of model-free implied volatility and exploits the observed VIX term structure to make inference on the unobserved spot volatility. We show that this new estimation method can be applied to a very general class of stochastic volatility models, such as one-factor or two-factor models. Moreover, the presence of jumps both in return and volatility processes does not affect our spot volatility estimates. In the second part of the study, we propose a simple and flexible extension of the Heston (1993) model and its multifactor affine versions: the addition of a deterministic volatility factor meant to automatically fit the term structure of model-free implied volatilities. When calibrated on daily panels of FX EURUSD options for 5 strikes (ATM, 25Δ and 10Δ) and 10 maturities (from one week to two years) in the period 2005-2012, we can obtain a pricing error (in terms of RMSE on implied volatility) of 0,167%, and never above 1,72%. The proposed class of models is then a suitable stochastic volatility candidate for fast and arbitrage-free interpolation of the volatility surface.

Aggregations and Marginalization of GARCH and Stochastic Volatility Models

MEDDAHI, Nour; RENAULT, Éric
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Artigo de Revista Científica Formato: 3570049 bytes; application/pdf
Relevância na Pesquisa
66.64%
The GARCH and Stochastic Volatility paradigms are often brought into conflict as two competitive views of the appropriate conditional variance concept : conditional variance given past values of the same series or conditional variance given a larger past information (including possibly unobservable state variables). The main thesis of this paper is that, since in general the econometrician has no idea about something like a structural level of disaggregation, a well-written volatility model should be specified in such a way that one is always allowed to reduce the information set without invalidating the model. To this respect, the debate between observable past information (in the GARCH spirit) versus unobservable conditioning information (in the state-space spirit) is irrelevant. In this paper, we stress a square-root autoregressive stochastic volatility (SR-SARV) model which remains true to the GARCH paradigm of ARMA dynamics for squared innovations but weakens the GARCH structure in order to obtain required robustness properties with respect to various kinds of aggregation. It is shown that the lack of robustness of the usual GARCH setting is due to two very restrictive assumptions : perfect linear correlation between squared innovations and conditional variance on the one hand and linear relationship between the conditional variance of the future conditional variance and the squared conditional variance on the other hand. By relaxing these assumptions...

Estimation of State Space Models and Stochastic Volatility

Miller Lira, Shirley
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Thèse ou Mémoire numérique / Electronic Thesis or Dissertation
EN
Relevância na Pesquisa
66.79%
Ma thèse est composée de trois chapitres reliés à l'estimation des modèles espace-état et volatilité stochastique. Dans le première article, nous développons une procédure de lissage de l'état, avec efficacité computationnelle, dans un modèle espace-état linéaire et gaussien. Nous montrons comment exploiter la structure particulière des modèles espace-état pour tirer les états latents efficacement. Nous analysons l'efficacité computationnelle des méthodes basées sur le filtre de Kalman, l'algorithme facteur de Cholesky et notre nouvelle méthode utilisant le compte d'opérations et d'expériences de calcul. Nous montrons que pour de nombreux cas importants, notre méthode est plus efficace. Les gains sont particulièrement grands pour les cas où la dimension des variables observées est grande ou dans les cas où il faut faire des tirages répétés des états pour les mêmes valeurs de paramètres. Comme application, on considère un modèle multivarié de Poisson avec le temps des intensités variables, lequel est utilisé pour analyser le compte de données des transactions sur les marchés financières. Dans le deuxième chapitre, nous proposons une nouvelle technique pour analyser des modèles multivariés à volatilité stochastique. La méthode proposée est basée sur le tirage efficace de la volatilité de son densité conditionnelle sachant les paramètres et les données. Notre méthodologie s'applique aux modèles avec plusieurs types de dépendance dans la coupe transversale. Nous pouvons modeler des matrices de corrélation conditionnelles variant dans le temps en incorporant des facteurs dans l'équation de rendements...

Simulation -based smoothing and filtering in factor stochastic volatility models : two econometric applications (July-2001)

Lopes, Hedibert Freitas
Fonte: Escola de Pós-Graduação em Economia da FGV Publicador: Escola de Pós-Graduação em Economia da FGV
Tipo: Relatório
EN_US
Relevância na Pesquisa
66.54%
The past decade has wítenessed a series of (well accepted and defined) financial crises periods in the world economy. Most of these events aI,"e country specific and eventually spreaded out across neighbor countries, with the concept of vicinity extrapolating the geographic maps and entering the contagion maps. Unfortunately, what contagion represents and how to measure it are still unanswered questions. In this article we measure the transmission of shocks by cross-market correlation\ coefficients following Forbes and Rigobon's (2000) notion of shift-contagion,. Our main contribution relies upon the use of traditional factor model techniques combined with stochastic volatility mo deIs to study the dependence among Latin American stock price indexes and the North American indexo More specifically, we concentrate on situations where the factor variances are modeled by a multivariate stochastic volatility structure. From a theoretical perspective, we improve currently available methodology by allowing the factor loadings, in the factor model structure, to have a time-varying structure and to capture changes in the series' weights over time. By doing this, we believe that changes and interventions experienced by those five countries are well accommodated by our models which learns and adapts reasonably fast to those economic and idiosyncratic shocks. We empirically show that the time varying covariance structure can be modeled by one or two common factors and that some sort of contagion is present in most of the series' covariances during periods of economical instability...

A continuous model and a discrete model for estimating the stochastic volatility probability density of financial series yields [Modelos discretos y continuos para estimar la densidad de probabilidad de la volatilidad estocástica de los rendimientos de series financieras]

Grajales Correa C.A.; Perez Ramirez F.O.
Fonte: Universidade de Medellín Publicador: Universidade de Medellín
Tipo: Article; info:eu-repo/semantics/article
SPA
Relevância na Pesquisa
56.63%
This article considers the daily yield of a financial asset for the purpose of modeling and comparing its stochastic volatility probability density. To do so, ARCH models and their extensions in discrete time are proposed as well as the empirical stochastic volatility mo-del developed by Paul Wilmott. For the discrete case, the models that enable estimating the conditional heterocedastic volatility in an instant t of time, t∈[1,T] are shown. For the continuous case, an Itô dissemination process is associated with the stochastic volatility of the financial series; that enables making said process discrete and simulating it, to obtain empirical volatility probability densities. Finally, the results are illustrated and compared to the methodologies discussed in the case of the financial series United Status S&P 500, the Mexican Stock Exchange Price and Quote Index (IPC is the Mexican acronym), and the Colombian Stock Exchange General Index (IGBC is the Colombian acronym).

A New Class of Stochastic Volatility Models with Jumps: Theory and Estimation

Chernov, Mikhail; Gallant, A. Ronald; Ghysels, Eric; Tauchen, George
Fonte: SSRN eLibrary Publicador: SSRN eLibrary
Tipo: Artigo de Revista Científica Formato: 499822 bytes; application/pdf
Publicado em //1999 EN_US
Relevância na Pesquisa
56.57%
The purpose of this paper is to propose a new class of jump diffusions which feature both stochastic volatility and random intensity jumps. Previous studies have focused primarily on pure jump processes with constant intensity and log-normal jumps or constant jump intensity combined with a one factor stochastic volatility model. We introduce several generalizations which can better accommodate several empirical features of returns data. In their most general form we introduce a class of processes which nests jump-diffusions previously considered in empirical work and includes the affine class of random intensity models studied by Bates (1998) and Duffie, Pan and Singleton (1998) but also allows for non-affine random intensity jump components. We attain the generality of our specification through a generic Levy process characterization of the jump component. The processes we introduce share the desirable feature with the affine class that they yield analytically tractable and explicit option pricing formula. The non-affine class of processes we study include specifications where the random intensity jump component depends on the size of the previous jump which represent an alternative to affine random intensity jump processes which feature correlation between the stochastic volatility and jump component. We also allow for and experiment with different empirical specifications of the jump size distributions. We use two types of data sets. One involves the S&P500 and the other comprises of 100 years of daily Dow Jones index. The former is a return series often used in the literature and allows us to compare our results with previous studies. The latter has the advantage to provide a long time series and enhances the possibility of estimating the jump component more precisely. The non-affine random intensity jump processes are more parsimonious than the affine class and appear to fit the data much better.

Detection of Patches of Outliers in Stochastic Volatility Processes.; Detection of Patches of Outliers in Stochastic Volatility Processes

Motta, Anderson C.O.; Hotta, Luiz K.
Fonte: Universidade de São Paulo. Instituto de Matemática e Estatística Publicador: Universidade de São Paulo. Instituto de Matemática e Estatística
Tipo: info:eu-repo/semantics/article; info:eu-repo/semantics/publishedVersion; ; ; Formato: application/pdf
Publicado em 12/12/2014 POR
Relevância na Pesquisa
66.71%
Because the volatility of nancial asset returns tends to arrive in clusters, it is quite likely that outliers appear in patches. In this case, most of the statistical tests developed to detect outliers have low power. We propose to use the posterior distribution of the size of the outlier and of the probability of the presence of an outlier at each observation to detect and estimate the outlier. This sampling algorithm is an adapted version of the algorithm proposed by Justel et al. (2001) for autoregressive time-series models. Our proposed sampling procedure is applied to a simulated sample according to the stochastic volatility, a sample of the New York Stock Exchange daily returns, and a sample of the Brazilian S~ao Paulo Stock Exchange daily returns.; Because the volatility of nancial asset returns tends to arrive in clusters, it is quite likely that outliers appear in patches. In this case, most of the statistical tests developed to detect outliers have low power. We propose to use the posterior distribution of the size of the outlier and of the probability of the presence of an outlier at each observation to detect and estimate the outlier. This sampling algorithm is an adapted version of the algorithm proposed by Justel et al. (2001) for autoregressive time-series models. Our proposed sampling procedure is applied to a simulated sample according to the stochastic volatility...