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Modelagem de volatilidade via modelos GARCH com erros assimétricos: abordagem Bayesiana; Volatility modeling through GARCH models with asymetric errors: Bayesian approach

Fioruci, José Augusto
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 12/06/2012 Português
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36.25%
A modelagem da volatilidade desempenha um papel fundamental em Econometria. Nesta dissertação são estudados a generalização dos modelos autorregressivos condicionalmente heterocedásticos conhecidos como GARCH e sua principal generalização multivariada, os modelos DCC-GARCH (Dynamic Condicional Correlation GARCH). Para os erros desses modelos são consideradas distribuições de probabilidade possivelmente assimétricas e leptocúrticas, sendo essas parametrizadas em função da assimetria e do peso nas caudas, necessitando assim de estimar esses parâmetros adicionais aos modelos. A estimação dos parâmetros dos modelos é feita sob a abordagem Bayesiana e devido às complexidades destes modelos, métodos computacionais baseados em simulações de Monte Carlo via Cadeias de Markov (MCMC) são utilizados. Para obter maior eficiência computacional os algoritmos de simulação da distribuição a posteriori dos parâmetros são implementados em linguagem de baixo nível. Por fim, a proposta de modelagem e estimação é exemplificada com dois conjuntos de dados reais; The modeling of volatility plays a fundamental role in Econometrics. In this dissertation are studied the generalization of known autoregressive conditionally heteroscedastic (GARCH) models and its main principal multivariate generalization...

Assimetrias na volatilidade e nas perturbações nos modelos de volatilidade; Leverage effect and asymmetry of the error distribution in volatility models

Daniel de Almeida
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 31/07/2013 Português
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36.49%
O objetivo da dissertação é estudar modelos de volatilidade que consideram dois tipos de assimetria usualmente encontradas em séries de finanças, a assimetria das perturbações e o efeito de alavancagem. Perturbações assimétricas são utilizadas devido ao fato estilizado de que perdas têm distribuição com cauda mais pesada do que ganhos. Já o efeito de alavancagem leva em consideração que perdas têm maior influência na volatilidade do que os ganhos. São estudados os modelos GARCH univariados que contemplam os dois tipos de assimetria separadamente e conjuntamente e modelos GARCH multivariados que permitem o efeito de alavancagem. Os resultados são apresentados em dois artigos. O primeiro descreve os principais modelos univariados que possam explicar estes dois fatos estilizados e analisa, com detalhes, oito séries: os índices Ibovespa, Merval e S&P 500, e as ações Itaú-Unibanco, Vale, Petrobras, Banco do Brasil e do Bradesco. A conclusão é que os dois tipos de assimetria estão presentes nas séries, na maioria das vezes simultaneamente. O segundo artigo faz uma revisão dos principais modelos multivariados da família GARCH, incluindo modelos com efeitos assimétricos nas variâncias e nas covariâncias condicionais. Alguns destes modelos são analisados com mais detalhes através de simulações. Considerou-se as perdas de eficiência na estimativa da matriz de volatilidade ao se ter erros de especificação...

Financial disclosure and stock price volatility: evidence from Portugal and Belgium

Vieira, Elisabete F. Simões; Pinho, Joaquim Carlos da Costa
Fonte: OTOC Publicador: OTOC
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
36.41%
This paper attempts to provide evidence on the determinants of reporting transparency and its impact on stock price volatility, analysing the disclosure practices of two European countries. We proxy for transparency by manually constructing two indexes scores for the sample firms. We assess the differences in disclosure practices between Portuguese firms and a matched sample of Belgian firms, applying a transparency and a volatility model. We find evidence that Portuguese firms are less transparent then the Belgian ones, concerning the subjects of ownership and governance. The results show that larger and more profitable firms are more transparent. For separate samples of Belgian and Portuguese firms, and based on annual reports information, we find no evidence of an association between transparency and price volatility. However, considering the quarterly reports, we find a negative relation between these variables for the second quarter, suggesting that the higher the transparency, the lower the stock price volatility. Analysing two small European countries with relative lack of research contributes to the recent literature on the information transparency investigating economic consequences of variations in disclosure (stock price volatility).

Transparency and stock price volatility: european evidence

Vieira, Elisabete F. Simões; Pinho, Joaquim Carlos da Costa
Fonte: Universidade de Aveiro Publicador: Universidade de Aveiro
Tipo: Conferência ou Objeto de Conferência
Português
Relevância na Pesquisa
36.41%
This paper studies the key determinants of the information transparency and its consequences for the market, namely in what concerns the stock price volatility, analysing the disclosure practices of two European countries. A transparency and a volatility model are applied. Based on annual reports information, we could not find any significant relationship between transparency and volatility. However, considering the quarterly reports, we find a negative relation between these variables for the second quarter, suggesting that the higher the transparency, the lower the stock price volatility. This research contributes to the recent literature on the information transparency and stock price volatility, analysing two small European countries that are clearly in need of research.

Assimetria na volatilidade dos principais índices bolsistas de Portugal, Irlanda, Itália, Grécia e Espanha : um estudo comparativo

Jerónimo, Sofia Ramos
Fonte: Instituto Politécnico de Lisboa Publicador: Instituto Politécnico de Lisboa
Tipo: Dissertação de Mestrado
Publicado em /02/2015 Português
Relevância na Pesquisa
36.62%
Mestrado em Controlo de Gestão e dos Negócios; A volatilidade desempenha um papel importante na avaliação dos activos financeiros. Existem vários estudos que concluem que a melhor análise de se prever a volatilidade deverá ser efectuada atendendo às especificidades do mercado financeiro onde se pretende fazer a previsão, permitindo assim captar momentos de grande incerteza no mercado. Verificam-se com frequência análises assimétricas na volatilidade, tais como: períodos de intensa volatilidade quando os preços dos activos sofrem quebras acentuadas, acréscimos de volatilidade em mercados que entram em aceleração, choques positivos e negativos sobre os preços que geram diferentes efeitos, sobre a volatilidade. Os efeitos da assimetria podem ser satisfatoriamente captados pelo modelo econométrico de tipo GARCH e, em especial por um dos modelos variantes, o modelo EGARCH. Este último é utilizado no presente estudo, onde se analisa o efeito assimétrico das rendibilidades dos índices de Portugal, Irlanda, Itália, Grécia e Espanha, durante o período 8 de Janeiro de 1990 a 3 de Janeiro de 2014, no sentido de ser estudado o efeito de alavancagem, sugerindo que os retornos negativos estão mais associados aos aglomerados de volatilidade...

Box-Jenkins and volatility models for Brazilian ‘Selic’ interest and currency rates

Ferreira, N. B.; Rocha, L.; Souza, A.; Santos, E.
Fonte: ExcellingTech Publisher Publicador: ExcellingTech Publisher
Tipo: Artigo de Revista Científica
Publicado em //2014 Português
Relevância na Pesquisa
36.25%
The use of statistical models in the analysis of macroeconomic variables is of principal importance since these models support the economic theory, as well as represent the actual behaviour of these variables. In this context, this research has as objective to describe the behaviour of Brazilian SELIC interest rates and foreign exchange from January 1974 to February 2014 and from January 1980 to February 2014, respectively. To accomplish this objective the Box-Jenkins methodology was used, where the analysis of residues showed the presence of heteroscedasticity. Then joint modelling was used to estimate the mean process by an ARIMA and the conditional variance by ARCH, GARCH, TARCH, EGARCH models. The results obtained showed SELIC interest rate series, was modelled by an ARIMA (1,1,1)-EGARCH (3, 1, 1) and, to the exchange rate the modelled fitted was an ARIMA(0,1,1)-EGARCH(1,1,1). It is evidenced through these models that there is asymmetry in the variables, yet there was the leverage effect. In addition, the volatility of these series in the context of Brazilian economic scenario revel the face of external and internal crises in the periods examined. So, the models fitted effectively captured the Brazilian economic behaviour during the period comprehended from 80´s to 90´s showing the mid degree of persistence of shocks like bad and good news...

THE LEVERAGE EFFECT AND THE ASYMMETRY OF THE ERROR DISTRIBUTION IN GARCH-BASED MODELS: THE CASE OF BRAZILIAN MARKET RELATED SERIES

Almeida,Daniel de; Hotta,Luiz K.
Fonte: Sociedade Brasileira de Pesquisa Operacional Publicador: Sociedade Brasileira de Pesquisa Operacional
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/08/2014 Português
Relevância na Pesquisa
36.28%
Traditional GARCH models fail to explain at least two of the stylized facts found in financial series: the asymmetry of the distribution of errors and the leverage effect. The leverage effect stems from the fact that losses have a greater influence on future volatilities than do gains. Asymmetry means that the distribution of losses has a heavier tail than the distribution of gains. We test whether these features are present in some series related to the Brazilian market. To test for the presence of these features, the series were fitted by GARCH(1,1), TGARCH(1,1), EGARCH(1,1), and GJR-GARCH(1,1) models with standardized Student t distribution errors with and without asymmetry. Information criteria and statistical tests of the significance of the symmetry and leverage parameters are used to compare the models. The estimates of the VaR (value-at-risk) are also used in the comparison. The conclusion is that both stylized facts are present in some series, mostly simultaneously.

How Does Public Information on Central Bank Intervention Strategies Affect Exchange Rate Volatility?

Mundaca, B. Gabriela
Fonte: Banco Mundial Publicador: Banco Mundial
Português
Relevância na Pesquisa
36.38%
Intervention operations in the foreign exchange market are used by the Banco Central de Reserva del Peru to manage both the level and volatility of their exchange rates. The Banco Central de Reserva del Peru provides information to the market about the specific hours of the day interventions would take place and the total amount of intervention. It consistently buys and sells on the foreign exchange market to avoid large appreciations and depreciations of the Peruvian nuevo sol against the U.S. dollar (Sol/USD), respectively. The estimates in this paper indicate that past information on interventions has moved the sol in the intended direction but only during the time the Banco Central de Reserva del Peru has announced it would be active in the foreign exchange market. The authors also find that the expectation of future interventions by the Banco Central de Reserva del Peru decreases the volatility of the sol when it intervenes to avoid an appreciation of the sol; however, the opposite occurs when the intervention takes place to defend the sol from depreciation. Indeed...

The sign of asymmetry and the Taylor Effect in stochastic volatility models

Veiga, Helena
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: Trabalho em Andamento Formato: application/pdf
Publicado em /02/2007 Português
Relevância na Pesquisa
36.49%
According to the Taylor-Effect the autocorrelations of absolute financial returns are higher than the ones of squared returns. In this work, we analyze this empirical property for three different asymmetric stochastic volatility models, with short and/or long memory. Specially, we investigate how the Taylor-Effect relates to the most important model characteristics: its asymmetry and its capacity to generate volatility persistence and kurtosis. Finally, we realize Monte Carlo experiments to infer about possible biases of the sample Taylor-Effect and fit the models to the return series of the Dow Jones.

Measuring causality between volatility and returns with high-frequency data

Dufour, Jean-Marie; García, René; Taamouti, Abderrahim
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: info:eu-repo/semantics/workingPaper; info:eu-repo/semantics/workingPaper Formato: application/pdf
Publicado em /09/2008 Português
Relevância na Pesquisa
46.67%
We use high-frequency data to study the dynamic relationship between volatility and equity returns. We provide evidence on two alternative mechanisms of interaction between returns and volatilities: the leverage effect and the volatility feedback effect. The leverage hypothesis asserts that return shocks lead to changes in conditional volatility, while the volatility feedback effect theory assumes that return shocks can be caused by changes in conditional volatility through a time-varying risk premium. On observing that a central difference between these alternative explanations lies in the direction of causality, we consider vector autoregressive models of returns and realized volatility and we measure these effects along with the time lags involved through short-run and long-run causality measures proposed in Dufour and Taamouti (2008), as opposed to simple correlations. We analyze 5-minute observations on S&P 500 Index futures contracts, the associated realized volatilities (before and after filtering jumps through the bispectrum) and implied volatilities. Using only returns and realized volatility, we find a weak dynamic leverage effect for the first four hours at the hourly frequency and a strong dynamic leverage effect for the first three days at the daily frequency. The volatility feedback effect appears to be negligible at all horizons. By contrast...

A nonparametric copula based test for conditional independence with applications to granger causality

Bouezmarni, Taoufik; Rombouts, Jeroen V. K.; Taamouti, Abderrahim
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: Trabalho em Andamento Formato: application/pdf
Publicado em /06/2009 Português
Relevância na Pesquisa
36.25%
This paper proposes a new nonparametric test for conditional independence, which is based on the comparison of Bernstein copula densities using the Hellinger distance. The test is easy to implement because it does not involve a weighting function in the test statistic, and it can be applied in general settings since there is no restriction on the dimension of the data. In fact, to apply the test, only a bandwidth is needed for the nonparametric copula. We prove that the test statistic is asymptotically pivotal under the null hypothesis, establish local power properties, and motivate the validity of the bootstrap technique that we use in finite sample settings. A simulation study illustrates the good size and power properties of the test. We illustrate the empirical relevance of our test by focusing on Granger causality using financial time series data to test for nonlinear leverage versus volatility feedback effects and to test for causality between stock returns and trading volume. In a third application, we investigate Granger causality between macroeconomic variables

Volatility models with Leverage effect

Rodríguez Villar, Mª José
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: Tese de Doutorado Formato: application/octet-stream; application/octet-stream; application/pdf
Português
Relevância na Pesquisa
36.65%
El objetivo de esta tesis es analizar y comparar la capacidad de algunos de los modelos habituales de series temporales para representar la volatilidad de las series financieras y sus características más importantes. En concreto, una de las principales consiste en que las series suelen presentan mayor número de observaciones extremas que las esperadas bajo Gausianidad. Además, las observaciones se agrupan de tal manera que tras movimientos grandes siguen movimientos grandes, mientras que por el contrario, cuando los movimientos comienzan a ser pequeños siguen siéndolo durante cierto tiempo. Este agrupamiento de volatilidad se refleja a través de la autocorrelación de cuadrados que suele ser significativa, positiva y presenta decaimiento exponencial. Finalmente, otra característica extensamente observada y propuesta por Black (1976) es la respuesta asimétrica de la volatilidad ante rendimientos positivos o negativos y conocida como leverage effect. En concreto, el incremento en la volatilidad es mayor cuando los retornos anteriores son negativos que cuando éstos son de la misma magnitud pero positivos. La presencia de este tipo de comportamiento se detecta en las correlaciones cruzadas entre rendimientos y rendimientos futuros al cuadrado...

Predicting the monthly volatility of the EuroStoxx 50 using data sampled at different frequencies

Ñíguez, Trino-Manuel
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 27/01/2008 Português
Relevância na Pesquisa
36.31%
This paper analyses the forecastability of the EuroStoxx 50 monthly returns volatil- ity. We consider different proxies for the unobserved volatility variable by using data sampled at di¤erent frequencies, and GARCH and AGARCH models with Normal and Student s t errors for the dynamics of returns conditional variance. We nd that a method based on aggregation of multi step (daily) ahead GARCH-type forecasts provide quite accurate predictions of monthly volatility.

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 Português
Relevância na Pesquisa
36.48%
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.

The effect of realised volatility on stock returns risk estimates

Grané, Aurea; Veiga, Helena
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: Trabalho em Andamento Formato: application/pdf; application/pdf; text/plain
Publicado em /09/2007 Português
Relevância na Pesquisa
36.35%
In this paper, we estimate minimum capital risk requirements for short, long positions and three investment horizons, using the traditional GARCH model and two other GARCH-type models that incorporate the possibility of asymmetric responses of volatility to price changes; and, most importantly, we analyse the models performance when realised volatility is included as an explanatory variable into the models' variance equations. The results suggest that the inclusion of realised volatility improves the models forecastability and their capacity to calculate accurate measures of minimum capital risk requirements.

Asymmetry and disorder: A decade of Parrondo's Paradox

Abbott, D.
Fonte: World Scientific Publishing Co. Pty. Ltd. Publicador: World Scientific Publishing Co. Pty. Ltd.
Tipo: Artigo de Revista Científica
Publicado em //2010 Português
Relevância na Pesquisa
36.3%
In 1996, Parrondo's games were first constructed using a simple coin tossing scenario, demonstrating the paradoxical situation where individually losing games combine to win. Parrondo's principle has become paradigmatic for situations where losing strategies or deleterious effects can combine to win. Intriguingly, there are deep connections between the Parrondo effect and a range of physical phenomena, as it turns out that Parrondo's original games are a discrete-time and discrete-space version of a flashing Brownian ratchet. This has been formally established via discretization of the Fokker–Planck equation. Over the past decade, many examples ranging from physics to population genetics have been reported in the literature pointing to the generality of Parrondo's principle. In general terms, the Parrondo effect occurs where there is a nonlinear interaction of random behavior with an asymmetry, and can be mathematically understood in terms of a convex linear combination. Many effects, where randomness plays a constructive role, such as stochastic resonance, volatility pumping, the Brazil nut paradox, etc., can be viewed as being in the class of Parrondian phenomena. We will briefly review the history of Parrondo's paradox, recent developments...

Positive skewness, anti-leverage, reverse volatility asymmetry, and short sale constraints: Evidence from the Chinese markets

Wu, Liang; Luo, Jingyi; Tang, Yingkai; Bardes, Gregory
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 05/11/2015 Português
Relevância na Pesquisa
46.65%
There are some statistical anomalies in the Chinese stock market, i.e., positive return skewness, anti-leverage effect (positive returns induce higher volatility than negative returns); and reverse volatility asymmetry (contemporaneous return-volatility correlation is positive). In this paper, we first confirm the existence of these anomalies using daily firm-level stock return data on the raw returns, excess returns and normalized excess returns. We empirically show that the asymmetry response of investors to news is one cause of the statistical anomalies if short sales are constrained. Then in the context of slow adoption of security lending policy, we conduct panel analysis and empirically verify that the lifting of short sale constraints leads to significantly less skewness, less anti-leverage effect and less reverse volatility asymmetry. Positive skewness is a feature of lottery. Investors are encouraged to bet on the upside lottery like potentials in the Chinese markets where the stocks skew more to the upside when short sales are constrained.; Comment: 26 pages, 3 figures, 4 tables

Daily House Price Indexes: Volatility Dynamics and Longer-Run Predictions

Wang, Wenjing
Fonte: Universidade Duke Publicador: Universidade Duke
Tipo: Dissertação
Publicado em //2014 Português
Relevância na Pesquisa
46.42%

This dissertation presents the construction procedure of “high-frequency” daily measure of changes in housing valuations, and analyzes its return dynamics, as well as investigates its relationship to capital markets. The dissertation consists of three chapters. The first chapter introduces the house price index methodologies and housing transaction data, and reviews the related literature. The second chapter shows the construction and modeling of daily house price indexes and highlights the informational advantage of the daily indexes. The final chapter provides detailed empirical and theoretical investigations of housing index return volatilities.

Chapter 2 discusses the relationship of the housing market with the other markets, such as consumer good market and financial markets. Different housing price indexes and their construction methodologies are introduced, with emphases on the repeat sales model and S&P/Case Shiller Home Price Index. A detailed description of the housing transaction data I use in the dissertation is also provided in this chapter.

Chapter 3 is co-authored with Professor Tim Bollerslev and Professor Andrew Patton. We construct daily house price indexes for ten major U.S. metropolitan areas. Our calculations are based on a comprehensive database of several million residential property transactions and a standard repeat-sales method that closely mimics the procedure used in the construction of the popular monthly Case-Shiller house price indexes. Our new daily house price indexes exhibit dynamic features similar to those of other daily asset prices...

Asymmetric Correlations in Financial Markets

Ozsoy, Sati Mehmet
Fonte: Universidade Duke Publicador: Universidade Duke
Tipo: Dissertação
Publicado em //2013 Português
Relevância na Pesquisa
26.85%

This dissertation consists of three essays on asymmetric correlations in financial markets. In the first essay, I have two main contributions. First, I show that dividend growth rates have symmetric correlations. Second, I show that asymmetric correlations are different than correlations being counter-cyclical. The correlation asymmetry I study in this dissertation should not be confused with correlations being counter-cyclical, i.e. being higher during recessions than during booms. I show that while counter-cyclical correlations can simply be explained by counter-cyclical aggregate market volatility, the correlation asymmetry with respect to joint upside and downside movements of returns are not just due to the heightened market volatility during those times.

In the second essay I present a model in order to explain the correlation asymmetry observed in the data. This is the first paper to offer an explanation for observed correlation asymmetry. I formalize the explanation using an equilibrium model. The model is useful to understand both the cross-section and time-series of correlation asymmetry. By the means of my model, we can answer questions about why some stocks have higher correlation asymmetry, and why the correlation asymmetry was higher during 1990s? In the model asset prices respond the realization of dividends and news about the future. However...

Assimetria na volatilidade dos retornos revisitada: Ibovespa, merval e inmex; Asymmetry of return volatility revisited: ibovespa, merval, and inmex

Otuki, Thiago Fleith; Radavelli, Carlos Henrique; Seabra, Fernando; Costa Jr., Newton Carneiro Affonso da
Fonte: Universidade de São Paulo. Faculdade de Economia, Administração e Contabilidade Publicador: Universidade de São Paulo. Faculdade de Economia, Administração e Contabilidade
Tipo: info:eu-repo/semantics/article; info:eu-repo/semantics/publishedVersion; ; ; ; ; ; Formato: application/pdf
Publicado em 01/12/2008 Português
Relevância na Pesquisa
36.47%
This paper searched, for evidence of the asymmetric effect on volatility in the stock index return series of Argentina (Merval), Brazil (Ibovespa), and Mexico (Inmex) from January 2000 to December 2005 using ARCH modeling. Results showed a greater influence of negative events on volatility than positive ones of the same intensity, and that shocks on the return series persisted for some time. This is similar to findings of Ceretta and Costa Jr. (1999) during the second half of the 1990 decade, a period with many financial crises. This comparison permits conjecture that this asymmetric effect does not depend upon whether the period in question was one with economic shocks or not.; Este artigo procura, por meio de modelos da classe ARCH, evidências do efeito assimétrico na volatilidade das séries de retornos dos índices de ações da Argentina (Merval), Brasil (Ibovespa) e México (Inmex) durante o período de janeiro de 2000 a dezembro de 2005. Os resultados mostraram maior influência de eventos negativos do que positivos, de mesma intensidade, sobre a volatilidade das séries analisadas, e verificou-se que choques nas séries de retornos têm efeito por vários períodos. Esses resultados são semelhantes aos encontrados por Ceretta e Costa Jr. (1999) para o período da segunda metade da década de 1990...