This thesis deals with stock modelling using ARCH and GARCH time series. Important aspect of stock modelling is to capture volatility correctly. Volatility in finance is usually defined as a standard deviation of asset returns. Many different models, which are summarized in the first part of this thesis, are used to model volatility. This thesis focus on multivariate volatility models including multivariate GARCH models. An approach to constructing a conditional maximum likelihood estimate to these methods is given. Discussed theory is applied on real financial data. In numeric application there is a construction of a volatility estimates for two specific stocks using models described in the first part of this thesis. Using the same financial data various bivariate models are compared. Based on comparison using maximum likelihood a specific model for these stocks is recommended. Powered by TCPDF (www.tcpdf.org)

O objetivo deste trabalho consiste em identificar a existência de contágio financeiro utilizando a metodologia de redes bayesianas. Além da rede bayesiana, a análise da interdependência de mercados internacionais em períodos de crises financeiras, ocorridas entre os anos 1996 e 2009, foi modelada com outras duas técnicas - modelos GARCH multivariados e de Cópulas, envolvendo países nos quais foi possível avaliar seus efeitos e que foram objetos de estudos similares na literatura. Com os períodos de crise bem definidos e metodologia calcada na teoria de grafos e na inferência bayesiana, executou-se uma análise sequencial, em que as realidades que precediam períodos de crise foram consideradas situações a priori para os eventos (verossimilhanças). Desta combinação resulta a nova realidade (a posteriori), que serve como priori para o período subsequente e assim por diante. Os resultados apontaram para grande interligação entre os mercados e diversas evidências de contágio em períodos de crise financeira, com causadores bem definidos e com grande respaldo na literatura. Ademais, os pares de países que apresentaram evidências de contágio financeiro pelas redes bayesianas em mais períodos de crises foram os mesmos que apresentaram os mais altos valores dos parâmetros estimados pelas cópulas e também aqueles cujos parâmetros foram mais fortemente significantes no modelo GARCH multivariado. Assim, os resultados obtidos pelas redes bayesianas tornam-se mais relevantes, o que sugere boa aderência deste modelo ao conjunto de dados utilizados neste estudo. Por fim, verificou-se que, após as diversas crises, os mercados estavam muito mais interligados do que no período inicialmente adotado. / This work aims to identify the existence of financial contagion using a metodology of Bayesian networks. Besides Bayesian networks, the analysis of the international markets\' interdependence in times of financial crises, occurred between 1996 and 2009, was modeled using two other techniques - multivariate GARCH models and Copulas models, involving countries in which its effects were possible to assess and which were subject to similar studies in the literature. With well-defined crisis periods and a metodology based on graph theory and Bayesian inference, a sequential analysis was executed, in which the realities preceding periods of crisis were considered to be prior situations to the events (likelihood). From this combination results the new posterior reality, which serves as a prior to the subsequent period and so on. The results pointed to a large interconnection between markets and several evidences of contagion in times of financial crises, with well-defined responsibles and highly supported by the literature. Moreover, the pairs of countries that show evidence of financial contagion by Bayesian networks in over periods of crises were the same as that presented the highest values of the parameters estimated by copulas and the most strongly significant parameters in the multivariate GARCH model. Thus, the results obtained by Bayesian networks become more relevant, suggesting good adherence of the model to the data set used in this study. Finally, it was found that after the various crises, the markets were much more connected.

[pt] Em Fleming, Kirby e Ostdiek (2001), encontram-se evidências de que a utilização de modelos de previsão da volatilidade, possui valor econômico significante quando se compara simplesmente com a matriz de variância incondicional, num arcabouço de otimização de portfólio. Indo além, este trabalho propõem averiguar se os modelos mais complexos de Correlação Condicional Constante (CCC) e Dinâmica (DCC) sugeridos respectivamente por Bollerslev (1990) e Engle (2002) podem oferecer melhores resultados. Os resultados encontrados são dependentes da preferência do investidor. Um investidor mais avesso ao risco, terá maior utilidade ao empregar o modelo DCC e CCC quando comparado ao simples modelo da média móvel com decaimento exponencial, popularizados por RiskMetrics. Isso ocorre porque os modelos DCC e CCC apresentam desvio padrão e retorno geralmente inferiores. Ainda, não é possível afirmar como em Fleming, Kirby e Ostdiek (2001) que a utilização de modelos de previsão da volatilidade, possui valor econômico significante. / [en] At Fleming, Kirby e Ostdiek (2001), evidences are found that volatility timming models, have signicant economic value when comparing with the simple unconditional variance matrix, in a framework of portfolio optimization. Going further, this work analyze if the more complex Constant (CCC) and Dynamic (DCC) Conditional Corrrelation models, suggested respectivily by Bollerslev (1990) and Engle (2002) can have a higher performance. The results found depend on the investor´s preference. A more risk averse investor has a higher utility level employing the DCC and CCC models when comparing with the simple exponencial moving avarage model, popularized by RiskMetrics. This happens because the DCC and CCC models usually have smaller standard deviation and return. Futhermore, it is not possible to assert, like at Fleming, Kirby e Ostdiek (2001), that volatility timming models have higher economic value.

Esta tese apresenta três ensaios em macroeconomia aplicada e que possuem em comum o uso de técnicas estatísticas e econométricas em problemas macroeconômicos. Dentre os campos de pesquisa da macroeconomia aplicada, a tese faz uso de modelos macroeconômicos microfundamentados, em sua versão DSGE-VAR, e da macroeconomia financeira por meio da avaliação do comportamento da correlação entre os retornos das ações usando modelos Garch multivariados. Além disso, a tese provoca a discussão sobre um novo campo de pesquisa em macroeconomia que surge a partir do advento da tecnologia. No primeiro ensaio, aplicamos a abordagem DSGE-VAR na discussão sobre a reação do Banco Central do Brasil (BCB) as oscilações na taxa de câmbio, especificamente para o caso de uma economia sob metas de inflação. Para tanto, baseando-se no modelo para uma economia aberta desenvolvido por Gali e Monacelli (2005) e modificado por Lubik e Schorfheide (2007), estimamos uma regra de política monetária para o Brasil e examinamos em que medida o BCB responde a mudanças na taxa de câmbio. Além disso, estudamos o grau de má especificação do modelo DSGE proposto. Mais especificamente, comparamos a verossimilhança marginal do modelo DSGE às do modelo DSGE-VAR e examinamos se o Banco Central conseguiu isolar a economia brasileira, em particular a inflação, de choques externos. Nossas conclusões mostram que as respostas aos desvios da taxa de câmbio são diferentes de zero e menores do que as respostas aos desvios da inflação. Finalmente, o ajuste do modelo DSGE é consideravelmente pior do que o ajuste do modelo DSGE-VAR, independentemente do número de defasagens utilizadas no VAR o que indica que de um ponto de vista estatístico existem evidências de que as restrições cruzadas do modelo teórico são violadas nos dados. O segundo ensaio examina empiricamente o comportamento da correlação entre o retorno de ações listadas na BMF&BOVESPA no período de 2000 a 2015. Para tanto, utilizamos modelos GARCH multivariados introduzidos por Bollerslev (1990) para extrair a série temporal das matrizes de correlação condicional dos retornos das ações. Com a série temporal dos maiores autovalores das matrizes de correlação condicional estimadas, aplicamos testes estatísticos (raiz unitária, quebra estrutural e tendência) para verificar a existência de tendência estocástica ou determinística para a intensidade da correlação entre os retornos das ações representadas pelos autovalores. Nossas conclusões confirmam que tanto em períodos de crises nacionais como turbulências internacionais, há intensificação da correlação entre as ações. Contudo, não encontramos qualquer tendência de longo prazo na série temporal dos maiores autovalores das matrizes de correlação condicional. Isso sugere que apesar das conclusões de Costa, Mazzeu e Jr (2016) sobre a tendência de queda do risco idiossincrático no mercado acionário brasileiro, a correlação dos retornos não apresentou tendência de alta, conforme esperado pela teoria de finanças. No terceiro ensaio, apresentamos pesquisas que utilizaram Big Data, Machine Learning e Text Mining em problemas macroeconômicos e discutimos as principais técnicas e tecnologias adotadas bem como aplicamos elas na análise de sentimento do BCB sobre a economia. Por meio de técnicas de Web Scraping e Text Mining, acessamos e extraímos as palavras usadas na escrita das atas divulgadas pelo Comitê de Política Monetária (Copom) no site do BCB. Após isso, comparando tais palavras com um dicionário de sentimentos (Inquider) mantido pela Universidade de Harvard e originalmente apresentado por Stone, Dunphy e Smith (1966), foi possível criar um índice de sentimento para a autoridade monetária. Nossos resultados confirmam que tal abordagem pode contribuir para a avaliação econômica dado que a série temporal do índice proposto está relacionada com variáveis macroeconômicas importantes para as decisões do BCB. / This thesis presents three essays in applied macroeconomics and who have in common the use of statistical and econometric techniques in macroeconomic problems. Among the search fields of applied macroeconomics, the thesis makes use of microfounded macroeconomic models, in tis DSGE-VAR version, and financial macroeconomics through the evaluation of the behavior of correlation between stock returns using multivariate Garch models. In addition, leads a discussion on a new field of research in macroeconomics which arises from the advent of technology. In the first experiment, we applied the approach to dynamic stochastic general equilibrium (DSGE VAR in the discussion about the reaction of the Central Bank of Brazil (CBB) to fluctuations in the exchange rate, specifically for the case of an economy under inflation targeting. To this end, based on the model for an open economy developed by Gali and Monacelli (2005) and modified by Lubik and Schorfheide (2007), we estimate a rule of monetary policy for the United States and examine to what extent the CBC responds to changes in the exchange rate. In addition, we studied the degree of poor specification of the DSGE model proposed. More specifically, we compare the marginal likelihood of the DSGE model to the DSGE-VAR model and examine whether the Central Bank managed to isolate the brazilian economy, in particular the inflation, external shocks. Our findings show that the response to deviations of the exchange rate are different from zero and lower than the response to deviations of inflation. Finally, the adjustment of the DSGE model is considerably worse than the adjustment of the DSGE-VAR model, regardless of the number of lags used in the VAR which indicates that a statistical point of view there is evidence that the restrictions crusades of the theoretical model are violated in the data. The second essay examines empirically the behavior of the correlation between the return of shares listed on the BMF&BOVESPA over the period from 2000 to 2015. To this end, we use models multivariate GARCH introduced by Bollerslev (1990) to remove the temporal series of arrays of conditional correlation of returns of stocks. With the temporal series of the largest eigenvalues of matrices of correlation estimated conditional, we apply statistical tests (unit root, structural breaks and trend) to verify the existence of stochastic trend or deterministic to the intensity of the correlation between the returns of the shares represented by eigenvalues. Our findings confirm that both in times of crises at national and international turbulence, there is greater correlation between the actions. However, we did not find any long-term trend in time series of the largest eigenvalues of matrices of correlation conditional. In the third test, we present research that used Big Data, Machine Learning and Text Mining in macroeconomic problems and discuss the main techniques and technologies adopted and apply them in the analysis of feeling of BCB on the economy. Through techniques of Web Scraping and Text Mining, we accessed and extracted the words used in the writing of the minutes released by the Monetary Policy Committee (Copom) on the site of the BCB. After that, comparing these words with a dictionary of feelings (Inquider) maintained by Harvard University and originally presented by Stone, Dunphy and Smith (1966), it was possible to create an index of sentiment for the monetary authority. Our results confirm that such an approach can contribute to the economic assessment given that the temporal series of the index proposed is related with macroeconomic variables are important for decisions of the BCB.

In this paper the performance of classical approaches and GARCH family models are evaluated and compared in estimation one-step-ahead VaR. The classical VaR methodology includes historical simulation (HS), RiskMetrics, and unconditional approaches. The classical VaR methods, the four univariate and two multivariate GARCH models with the Student’s t and the normal error distributions have been applied to 5 stock indices and 4 portfolios to determine the best VaR method. We used four evaluation tests to assess the quality of VaR forecasts: -                     Violation ratio -                     Kupiec’s test -                     Christoffersen’s test -                     Joint test The results point out that GARCH-based models produce far more accurate forecasts for both individual and portfolio VaR. RiskMetrics gives reliable VaR predictions but it is still substantially inferior to GARCH models. The choice of an optimal GARCH model depends on the individual asset, and the best model can be different based on different empirical data.

The global foreign exchange market is the largest financial market with turnover in this market often outstripping the GDP of countries in which they are located. The dynamics in the foreign exchange market, especially price dynamics, have huge implications for financial asset values, financial returns and volatility in the international financial system. It is therefore an important area of study. Exchange rates have often departed significantly from the level implied by fundamentals and exhibit excessive volatility. This reality creates a role for central bank intervention in this market to keep the rate in line with economic fundamentals and the overall policy mix, to stabilize market expectations and to calm disorderly markets. Studies that attempt to measure the effectiveness of intervention in the foreign exchange market in terms of exchange rate trends and volatility have had mixed results. This, in many cases, reflects the unavailability of data and the weaknesses in the empirical frameworks used to measure effectiveness. This thesis utilises the most recent data available and some of the latest methodological advances to measure the effectiveness of central bank intervention in the foreign exchange markets of a variety of countries. It therefore makes a contribution in the area of applied empirical methodologies for the measurement of the dynamics of intervention in the foreign exchange market. It demonstrates that by using high frequency data and more robust and appropriate empirical methodologies central bank intervention in the foreign exchange market can be effective. Moreover, a framework that takes account of the interactions between different central bank policy instruments and price dynamics, the reaction function of the central bank, different states of the market, liquidity in the market and the profitability of the central bank can improve the effectiveness of measuring the impact of central bank policy in the foreign exchange market and provide useful information to policy makers.

This dissertation consists of three essays. In the first essay, I estimate a high dimensional covariance matrix of returns for 88 individual stocks from the S&P 100 index, using daily return data for 1995-2005. This study applies the two-step estimator of the dynamic conditional correlation multivariate GARCH model, proposed by Engle (2002b) and Engle and Sheppard (2001) and applies variations of this model. This is the first study estimating variances and covariances of returns using a large number of individual stocks (e.g., Engle and Sheppard (2001) use data on various aggregate sub-indexes of stocks). This avoids errors in estimation of GARCH models with contemporaneous aggregation of stocks (e.g. Nijman and Sentana 1996; Komunjer 2001). Second, this is the first multivariate GARCH adopting a systematic general-to-specific approach to specification of lagged returns in the mean equation. Various alternatives to simple GARCH are considered in step one univariate estimation, and econometric results favour an asymmetric EGARCH extension of Engle and Sheppard’s model. In essay two, I aggregate a variance-covariance matrix of return risk (estimated using DCC-MVGARCH in essay one) to an aggregate index of return risk. This measure of risk is compared with the standard approach to measuring risk from a simple univariate GARCH model of aggregate returns. In principle the standard approach implies errors in estimation due to contemporaneous aggregation of stocks. The two measures are compared in terms of correlation and economic values: measures are not perfectly correlated, and the economic value for the improved estimate of risk as calculated here is substantial. Essay three has three parts. The major part is an empirical study of the aggregate risk return tradeoff for U.S. stocks using daily data. Recent research indicates that past risk-return studies suffer from inadequate sample size, and this suggests using daily rather than monthly data. Modeling dynamics/lags is critical in daily models, and apparently this is the first such study to model lags correctly using a general to specific approach. This is also the first risk return study to apply Wu tests for possible problems of endogeneity/measurement error for the risk variable. Results indicate a statistically significant positive relation between expected returns and risk, as is predicted by capital asset pricing models. Development of the Wu test leads naturally into a model relating aggregate risk of returns to economic variables from the risk return study. This is the first such model to include lags in variables based on a general to specific methodology and to include covariances of such variables. I also derive coefficient links between such models and risk-return models, so in theory these models are more closely related than has been realized in past literature. Empirical results for the daily model are consistent with theory and indicate that the economic and financial variables explain a substantial part of variation in daily risk of returns. The first section of this essay also investigates at a theoretical and empirical level several alternative index number approaches for aggregating multivariate risk over stocks. The empirical results indicate that these indexes are highly correlated for this data set, so only the simplest indexes are used in the remainder of the essay.

This dissertation consists of three essays. In the first essay, I estimate a high dimensional covariance matrix of returns for 88 individual stocks from the S&P 100 index, using daily return data for 1995-2005. This study applies the two-step estimator of the dynamic conditional correlation multivariate GARCH model, proposed by Engle (2002b) and Engle and Sheppard (2001) and applies variations of this model. This is the first study estimating variances and covariances of returns using a large number of individual stocks (e.g., Engle and Sheppard (2001) use data on various aggregate sub-indexes of stocks). This avoids errors in estimation of GARCH models with contemporaneous aggregation of stocks (e.g. Nijman and Sentana 1996; Komunjer 2001). Second, this is the first multivariate GARCH adopting a systematic general-to-specific approach to specification of lagged returns in the mean equation. Various alternatives to simple GARCH are considered in step one univariate estimation, and econometric results favour an asymmetric EGARCH extension of Engle and Sheppard’s model. In essay two, I aggregate a variance-covariance matrix of return risk (estimated using DCC-MVGARCH in essay one) to an aggregate index of return risk. This measure of risk is compared with the standard approach to measuring risk from a simple univariate GARCH model of aggregate returns. In principle the standard approach implies errors in estimation due to contemporaneous aggregation of stocks. The two measures are compared in terms of correlation and economic values: measures are not perfectly correlated, and the economic value for the improved estimate of risk as calculated here is substantial. Essay three has three parts. The major part is an empirical study of the aggregate risk return tradeoff for U.S. stocks using daily data. Recent research indicates that past risk-return studies suffer from inadequate sample size, and this suggests using daily rather than monthly data. Modeling dynamics/lags is critical in daily models, and apparently this is the first such study to model lags correctly using a general to specific approach. This is also the first risk return study to apply Wu tests for possible problems of endogeneity/measurement error for the risk variable. Results indicate a statistically significant positive relation between expected returns and risk, as is predicted by capital asset pricing models. Development of the Wu test leads naturally into a model relating aggregate risk of returns to economic variables from the risk return study. This is the first such model to include lags in variables based on a general to specific methodology and to include covariances of such variables. I also derive coefficient links between such models and risk-return models, so in theory these models are more closely related than has been realized in past literature. Empirical results for the daily model are consistent with theory and indicate that the economic and financial variables explain a substantial part of variation in daily risk of returns. The first section of this essay also investigates at a theoretical and empirical level several alternative index number approaches for aggregating multivariate risk over stocks. The empirical results indicate that these indexes are highly correlated for this data set, so only the simplest indexes are used in the remainder of the essay.

This paper examines return co-movements and volatility spillovers between major exchange rates before and after the introduction of euro. Dynamic correlations and VAR-based spillover index results suggest significant return co-movements and volatility spillovers, however, their extend is, on average, lower in the post-euro period. Co-movements and spillovers are positively associated with extreme episodes and US dollar appreciations. The euro (Deutsche mark) is the dominant net transmitter of volatility, while the British pound the dominant net receiver of volatility in both periods. Nevertheless, cross-market volatility spillovers are bidirectional, and the highest spillovers occur between European markets. (author's abstract)

[pt] O apreçamento de opções é um assunto muito importante nos dias de hoje. Métodos probabilisticos são necessários para fazer o apreçamento neutro ao risco. Usaremos o método de Siu et al. para duas classes de GARCHs, o FC-GARCH e a mistura de GARCHs Em ambos os modelos nós encontramos a versão neutra ao risco do modelo que é necessária para a precificação de contratos, em dois diferentes casos, quando o ruído é normal e quando é shifted gamma. Fizemos também simulações para ilustrar e comparamos os resultados com o valor de Black Scholes, verificamos a existência de smile e fizemos uma análise de sensibilidade nos parâmetros. / [en] Option pricing is a very important issue nowadays. The use of probabilistic methods is required for risk neutral pricing. Here we apply the method of Siu et al. for two classes of GARCHs, viz., the FC-GARCH and the Mixture of GARCHs. In both models we derive the risk neutral version of the model which is essential for pricing contracts, in two different cases, when the noise is normal as well as when it is shifted gamma. We also performed simulations with both models and compared to the benchmark Black Scholes model, checked for the smile effect and made some sensibility analysis in the parameters.