The modelling of volatility has long been seminal to finance and risk management in general, as it provides information on the spread of portfolio returns. In order to reduce the overall volatility of a stock portfolio, modern portfolio theory (MPT), within an efficient market hypothesis (EMH) framework, dictates that a well-diversified portfolio should have a market beta of one (thereafter adjusted for risk preference), and thus move in sync with a benchmark market portfolio. Such a stock portfolio is highly correlated with the market, and considered to be entirely hedged against unsystematic risk. However, the risks within and between stocks present in a portfolio still impact on each other. In particular, risk present in a particular stock may spill over and affect the risk profile of another stock included within a portfolio - a phenomenon known as volatility spill-over effects. In developing economies such as South Africa, portfolio managers are limited in their choices of stocks. This increases the difficulty of fully diversifying a stock portfolio given the volatility spill-over effects that may be present between stocks listed on the same exchange. In addition, stock portfolios are not static, and therefore require constant rebalancing according to the mandate of the managing fund. The process of constant rebalancing of a stock portfolio (for instance, to follow the market) becomes more complex and difficult during times of financial distress. Considering all these conditions, portfolio managers need all the relevant information (more than MPT would provide) available to them in order to select and rebalance a portfolio of stocks that are as mean-variance efficient as possible. This study provides an additional measure to market beta in order to construct a more efficient portfolio. The additional measure analyse the volatility spill-over effects between stocks within the same portfolio. Using intraday stock returns and a residual based test (aggregate shock [AS] model), volatility spill-over effects are estimated between stocks. It is shown that when a particular stock attracts fewer spill-over effects from the other stocks in the portfolio, the overall portfolio volatility would decrease as well. In most cases market beta showcased similar results; this change is however not linear in the case of market beta. Therefore, in order to construct a more efficient portfolio, one requires both a portfolio that has a unit correlation with the market, but also includes stocks with the least amount of volatility spill-over effects among each other. / MCom (Risk Management), North-West University, Potchefstroom Campus, 2013

The modelling of volatility has long been seminal to finance and risk management in general, as it provides information on the spread of portfolio returns. In order to reduce the overall volatility of a stock portfolio, modern portfolio theory (MPT), within an efficient market hypothesis (EMH) framework, dictates that a well-diversified portfolio should have a market beta of one (thereafter adjusted for risk preference), and thus move in sync with a benchmark market portfolio. Such a stock portfolio is highly correlated with the market, and considered to be entirely hedged against unsystematic risk. However, the risks within and between stocks present in a portfolio still impact on each other. In particular, risk present in a particular stock may spill over and affect the risk profile of another stock included within a portfolio - a phenomenon known as volatility spill-over effects. In developing economies such as South Africa, portfolio managers are limited in their choices of stocks. This increases the difficulty of fully diversifying a stock portfolio given the volatility spill-over effects that may be present between stocks listed on the same exchange. In addition, stock portfolios are not static, and therefore require constant rebalancing according to the mandate of the managing fund. The process of constant rebalancing of a stock portfolio (for instance, to follow the market) becomes more complex and difficult during times of financial distress. Considering all these conditions, portfolio managers need all the relevant information (more than MPT would provide) available to them in order to select and rebalance a portfolio of stocks that are as mean-variance efficient as possible. This study provides an additional measure to market beta in order to construct a more efficient portfolio. The additional measure analyse the volatility spill-over effects between stocks within the same portfolio. Using intraday stock returns and a residual based test (aggregate shock [AS] model), volatility spill-over effects are estimated between stocks. It is shown that when a particular stock attracts fewer spill-over effects from the other stocks in the portfolio, the overall portfolio volatility would decrease as well. In most cases market beta showcased similar results; this change is however not linear in the case of market beta. Therefore, in order to construct a more efficient portfolio, one requires both a portfolio that has a unit correlation with the market, but also includes stocks with the least amount of volatility spill-over effects among each other. / MCom (Risk Management), North-West University, Potchefstroom Campus, 2013

Cette thèse tente d'évaluer l'intégration des marchés émergents dans une perspective régionale et intra-régionale. Elle contribue à la littérature existante en développant un modèle dynamique d’évaluation des actifs financiers à l’international (ICAPM) avec changement de régime. Spécifiquement, les rentabilités attendues peuvent passer du régime de segmentation parfaite au régime d’intégration parfaite ou inversement en fonction d’un certain nombre de facteurs nationaux, régionaux et internationaux qui sont susceptibles d’influencer le processus d’intégration financière. Le champ d’étude s’étend aux pays de l’Asie de Sud-est, d’Europe Sud-est, de l’Amérique Latine et du Moyen Orient sur la période 1996-2008. Nous développons le modèle de Bekaert et Harvey (1995) où la PPA n’est pas vérifiée, et les variances et covariances conditionnelles sont modélisées grâce à un processus GARCH multivarié. Cette approche permet de déterminer simultanément le niveau d’intégration au cours du temps de toutes les zones dans le marché mondial et le niveau d’intégration intra-régionale dans chaque région. Il permet aussi d’analyser la formation de la prime de risque totale. Nos résultats empiriques montrent que les marchés émergents restent encore très segmentés du marché mondial et des marchés régionaux. Ces résultats suggèrent que l’inclusion des actifs des marchés émergents continue à générer des gains de diversification substantiels, et que les règles d’évaluation devraient être conformes à un état d’intégration partielle. / The purpose of this thesis is to study the dynamics of the global integration process of four emerging market regions into the world and the regional market, while taking into account the importance of exchange rate and local market risk. An international capital asset pricing model suitable for partially integrated markets and departure from purchasing power parity was developed in the spirit of Bekaert and Harvey (1995)’s regime-switching model in order to explain the time-variations in expected returns on regional emerging market indices. In its fully functional form, the model allows the market integration measure as well as the global and local risk premiums to vary through time. We mainly find that the integration degree in emerging market regions (Latin America, Asia, Southeastern Europe, and the Middle East) varied widely through time over the period 1996-2008 and is satisfactorily explained by global, regional and national factors. Even though it reaches fairly high values during several periods, and exhibit an upward trend towards the end of the estimation period, the emerging market regions under consideration still remain segmented from the world and regional market. These results thus suggest that diversification into emerging market assets continue to produce substantial profits and that the asset pricing rules should reflect a state of partial integration. Our investigation, which addresses the evolution and formation of total risk premiums, confirm this empirically.

A volatilidade é uma medida de incerteza quanto às variações dos preços de ativos. Este trabalho tem como objetivo analisar a volatilidade, através dos diversos modelos da família GARCH, de três índices de mercados financeiros: Dow Jones, IBovespa e S&P 500. Com este intuito, foram aqui utilizadas técnicas univariadas e multivariadas, bem como análises de Causalidade de Granger. Através das duas primeiras ferramentas, escolhemos o melhor modelo para cada um destes casos. Usando a terceira ferramenta, concluímos que o IBovespa é significativamente influenciado pela abertura do Dow Jones e do S&P500. Por outro lado, mostramos que a abertura do IBovespa não impacta, nem à 10% de significância, os índices Dow Jones e S&P 500. Também concluímos que a incorporação de um dos índices americanos ao modelo do IBovespa torna-o mais significativo, uma vez que o mercado acionário brasileiro é impactado pelos dois índices citados anteriormente. Desta forma, este trabalho mostra que os modelos GARCH multivariados aparentam ser mais eficazes na estimação da volatilidade de ativos financeiros do que os modelos GARCH univariados. / The volatility is a measure of the uncertainty of variations of asset prices. The main goal of this work is to analyze the volatility, by the use of several models of the GARCH family, of three financial market indexes: Dow Jones, IBovespa and S&P 500. With this purpose, we use univariate and multivariate techniques, as well as Granger Causality. Using these first two tools, we choose the best model for each one of these cases. Using the third tool, we conclude that the IBovespa is significatively influenced by the opening of the Dow Jones and the S&P 500 indexes. On the other hand, we show that the opening of the IBovespa does not impact, not even at 10% of significance, the Dow Jones and S&P 500 indexes. We also conclude that incorporation of one of these American indexes to the model involving IBovespa makes it more significant, once the Brazilian Stock Market is impacted by the two American indexes we mention before. This work shows that multivariate GARCH models seem to be more efficient in the volatility estimation of financial assets than univariate GARCH models.

Submitted by Marcia Bacha (marcia.bacha@fgv.br) on 2012-03-07T12:45:08Z No. of bitstreams: 1 20120306084421880.pdf: 1716342 bytes, checksum: e7f9f7df4b67ff4e12f57770620942d8 (MD5) / Approved for entry into archive by Gisele Isaura Hannickel (gisele.hannickel@fgv.br) on 2012-03-07T12:50:42Z (GMT) No. of bitstreams: 1 20120306084421880.pdf: 1716342 bytes, checksum: e7f9f7df4b67ff4e12f57770620942d8 (MD5) / Made available in DSpace on 2012-03-07T12:51:26Z (GMT). No. of bitstreams: 1 20120306084421880.pdf: 1716342 bytes, checksum: e7f9f7df4b67ff4e12f57770620942d8 (MD5) / Com origem no setor imobiliário americano, a crise de crédito de 2008 gerou grandes perdas nos mercados ao redor do mundo. O mês de outubro do mesmo ano concentrou a maior parte da turbulência, apresentando também uma explosão na volatilidade. Em meados de 2006 e 2007, o VIX, um índice de volatilidade implícita das opções do S&P500, registrou uma elevação de patamar, sinalizando o possível desequilíbrio existente no mercado americano. Esta dissertação analisa se o consenso de que a volatilidade implícita é a melhor previsora da volatilidade futura permanece durante o período de crise. Os resultados indicam que o VIX perde poder explicativo ao se passar do período sem crise para o de crise, sendo ultrapassado pela volatilidade realizada. / Started in the U.S. housing sector, the credit crisis of 2008 caused great damage in markets around the world. The effects were concentrated in October of the same year, which also showed an explosion in volatility. In mid-2006 and mid-2007, the VIX, an index of implied volatility of options on the S&P500, recorded a rise in level signaling the possible imbalance in the U.S. market. This dissertation examines whether the consensus that implied volatility is the best predictor of future volatility remains during the crisis. The results indicate that the VIX loses explanatory power to move from a period of economic stability for a period of crisis, been surpassed by the realized volatility.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / As instituições financeiras são obrigadas por acordos internacionais, como o Acordo de Basiléia, a avaliar o risco de mercado ao qual a instituição está propensa de forma a evitar possíveis contaminações de desastres financeiros em seu patrimônio. Com o intuito de capturar tais fenômenos, surge a necessidade de construir modelos que capturem com mais acurácia movimentos extremos das séries de retornos. O trabalho teve como principal objetivo aplicar a Teoria do Valor Extremo juntamente com Copulas na estimação de quantis extremos para o VaR. Ele utiliza técnicas de simulação de Monte Carlo, Teoria do Valor Extremo e Cópulas com distribuições gaussianas e t. Em contrapartida, as estimativas produzidas serão comparadas com as de um segundo modelo, chamado de simulação histórica de Monte Carlo filtrada, mais conhecida como filtered historical simulation (FHS). As técnicas serão aplicadas a um portfólio de ações de empresas brasileiras. / Financial institutions are required by international agreements such as the Basel Accord, to assess the market risk to which the institution is likely to avoid possible contamination of its assets in financial disasters. In order to capture these phenomena, the need arises to build models that more accurately capture extreme movements of the return series. The work aimed to apply the Extreme Value Theory along with the estimation of copulas for VaR extremes quantiles. He uses techniques of Monte Carlo simulation, Extreme Value Theory and Copulas with Gaussian and t distributions. In contrast, the estimates produced will be compared with a second model, called Monte Carlo simulation of historical filtered, better known as filtered historical simulation (FHS). The techniques are applied to a portfolio of stocks of Brazilian companies.

A volatilidade é uma medida de incerteza quanto às variações dos preços de ativos. Este trabalho tem como objetivo analisar a volatilidade, através dos diversos modelos da família GARCH, de três índices de mercados financeiros: Dow Jones, IBovespa e S&P 500. Com este intuito, foram aqui utilizadas técnicas univariadas e multivariadas, bem como análises de Causalidade de Granger. Através das duas primeiras ferramentas, escolhemos o melhor modelo para cada um destes casos. Usando a terceira ferramenta, concluímos que o IBovespa é significativamente influenciado pela abertura do Dow Jones e do S&P500. Por outro lado, mostramos que a abertura do IBovespa não impacta, nem à 10% de significância, os índices Dow Jones e S&P 500. Também concluímos que a incorporação de um dos índices americanos ao modelo do IBovespa torna-o mais significativo, uma vez que o mercado acionário brasileiro é impactado pelos dois índices citados anteriormente. Desta forma, este trabalho mostra que os modelos GARCH multivariados aparentam ser mais eficazes na estimação da volatilidade de ativos financeiros do que os modelos GARCH univariados. / The volatility is a measure of the uncertainty of variations of asset prices. The main goal of this work is to analyze the volatility, by the use of several models of the GARCH family, of three financial market indexes: Dow Jones, IBovespa and S&P 500. With this purpose, we use univariate and multivariate techniques, as well as Granger Causality. Using these first two tools, we choose the best model for each one of these cases. Using the third tool, we conclude that the IBovespa is significatively influenced by the opening of the Dow Jones and the S&P 500 indexes. On the other hand, we show that the opening of the IBovespa does not impact, not even at 10% of significance, the Dow Jones and S&P 500 indexes. We also conclude that incorporation of one of these American indexes to the model involving IBovespa makes it more significant, once the Brazilian Stock Market is impacted by the two American indexes we mention before. This work shows that multivariate GARCH models seem to be more efficient in the volatility estimation of financial assets than univariate GARCH models.

[pt] A presente tese é composta por três pesquisas. A primeira pesquisa buscou averiguar o relacionamento entre o FXvol e os retornos futuros da taxa cambial e do índice de mercado de ações, dado que o índice de volatilidade FXvol é visto como um termômetro da incerteza do investidor um período a frente. Investiga-se então a relação contemporânea entre o FXvol, a Ptax e o Ibovespa, bem como a capacidade do FXvol de captar a possível relação entre o nível de incerteza presente no mercado e as variações relativas futuras da taxa de câmbio e do índice de ações. A segunda pesquisa comparou os modelos GARCH tradicionais e o modelo GARCH com troca de regimes no que tange seu poder de previsão da volatilidade cambial. Buscou-se comparar o desempenho de cada um dos modelos em uma situação real de utilização, no caso, no cálculo do Valor em Risco de uma carteira cambial. A terceira pesquisa buscou identificar a existência do efeito manada no mercado brasileiro e compreender a influência do câmbio nesse efeito, devido à importância do mercado cambial para a realidade brasileira. A metodologia compreendeu dois passos, em um primeiro momento buscou-se analisar a média do efeito através de regressões tradicionais e num segundo momento estudar a variação do efeito ao longo do tempo através do método do Filtro de Kalman. / [en] The present thesis consists of three researches. The first research sought to ascertain the relationship between FXvol and future exchange rate and stock market index returns as the FXvol volatility index is viewed as a thermometer of investor uncertainty for a period ahead. The contemporary relationship between FXvol, Ptax and Ibovespa, as well as the ability of FXvol to capture the possible relationship between the level of uncertainty present in the market and the relative future return of the exchange rate and the stock index. The second research compared the traditional GARCH models and the GARCH model with regime changes regarding its power to predict the exchange rate volatility. We attempted to compare the performance of each of the models in a real situation of use, in this case, in the calculation of the Value at Risk of an exchange portfolio. The third research sought to identify the existence of the herd effect in the Brazilian market and to understand the influence of the exchange rate in this effect, due to the importance of the exchange market for the Brazilian market. The methodology comprised two steps, initially attempting to analyze the mean of the effect through regressions and in a second moment to study the variation of the effect over time through the Kalman Filter method.

Submitted by Bruna Rodrigues (bruna92rodrigues@yahoo.com.br) on 2017-09-27T14:34:29Z No. of bitstreams: 1 DissKFAG.pdf: 21371434 bytes, checksum: e9355d67b5b05eda13ae02e3ae7d0fdf (MD5) / Approved for entry into archive by Ronildo Prado (bco.producao.intelectual@gmail.com) on 2018-01-30T19:20:29Z (GMT) No. of bitstreams: 1 DissKFAG.pdf: 21371434 bytes, checksum: e9355d67b5b05eda13ae02e3ae7d0fdf (MD5) / Approved for entry into archive by Ronildo Prado (bco.producao.intelectual@gmail.com) on 2018-01-30T19:20:37Z (GMT) No. of bitstreams: 1 DissKFAG.pdf: 21371434 bytes, checksum: e9355d67b5b05eda13ae02e3ae7d0fdf (MD5) / Made available in DSpace on 2018-01-30T19:26:17Z (GMT). No. of bitstreams: 1 DissKFAG.pdf: 21371434 bytes, checksum: e9355d67b5b05eda13ae02e3ae7d0fdf (MD5) Previous issue date: 2017-07-18 / Não recebi financiamento / In the last decades volatility has become a very important concept in the financial area, being used to measure the risk of financial instruments. In this work, the focus of study is the modeling of volatility, that refers to the variability of returns, which is a characteristic present in the financial time series. As a fundamental modeling tool, we used the GARCH (Generalized Autoregressive Conditional Heteroskedasticity) model, which uses conditional heteroscedasticity as a measure of volatility. Two main characteristics will be considered to be modeled with the purpose of a better adjustment and prediction of the volatility, these are: heavy tails and an asymmetry present in the unconditional distribution of the return series. The estimation of the parameters of the proposed models is done by means of the Bayesian approach with an MCMC (Markov Chain Monte Carlo) methodology , specifically the Metropolis-Hastings algorithm. / Nas últimas décadas a volatilidade transformou-se num conceito muito importante na área financeira, sendo utilizada para mensurar o risco de instrumentos financeiros. Neste trabalho, o foco de estudo é a modelagem da volatilidade, que faz referência à variabilidade dos retornos, sendo esta uma característica presente nas séries temporais financeiras. Como ferramenta fundamental da modelação usaremos o modelo GARCH (Generalized Autoregressive Conditional Heteroskedasticity), que usa a heterocedasticidade condicional como uma medida da volatilidade. Considerar-se-ão duas características principais a ser modeladas com o propósito de obter um melhor ajuste e previsão da volatilidade, estas são: a assimetria e as caudas pesadas presentes na distribuição incondicional da série dos retornos. A estimação dos parâmetros dos modelos propostos será feita utilizando a abordagem Bayesiana com a metodologia MCMC (Markov Chain Monte Carlo) especificamente o algoritmo de Metropolis-Hastings.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / As instituições financeiras são obrigadas por acordos internacionais, como o Acordo de Basiléia, a avaliar o risco de mercado ao qual a instituição está propensa de forma a evitar possíveis contaminações de desastres financeiros em seu patrimônio. Com o intuito de capturar tais fenômenos, surge a necessidade de construir modelos que capturem com mais acurácia movimentos extremos das séries de retornos. O trabalho teve como principal objetivo aplicar a Teoria do Valor Extremo juntamente com Copulas na estimação de quantis extremos para o VaR. Ele utiliza técnicas de simulação de Monte Carlo, Teoria do Valor Extremo e Cópulas com distribuições gaussianas e t. Em contrapartida, as estimativas produzidas serão comparadas com as de um segundo modelo, chamado de simulação histórica de Monte Carlo filtrada, mais conhecida como filtered historical simulation (FHS). As técnicas serão aplicadas a um portfólio de ações de empresas brasileiras. / Financial institutions are required by international agreements such as the Basel Accord, to assess the market risk to which the institution is likely to avoid possible contamination of its assets in financial disasters. In order to capture these phenomena, the need arises to build models that more accurately capture extreme movements of the return series. The work aimed to apply the Extreme Value Theory along with the estimation of copulas for VaR extremes quantiles. He uses techniques of Monte Carlo simulation, Extreme Value Theory and Copulas with Gaussian and t distributions. In contrast, the estimates produced will be compared with a second model, called Monte Carlo simulation of historical filtered, better known as filtered historical simulation (FHS). The techniques are applied to a portfolio of stocks of Brazilian companies.