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.

This study explores the dynamics between stock price and exchange rates through the cointegration methodology proposed by Herwartz and Luetkepohl (2011). Moreover, it consider the vector error correction model (VECM) with conditional heteroscedastic variance. And we use a feasible generalized least squares (FGLS) estimator to estimate the cointegrating vector. This paper analysis some Asian countries' data from 1997 to 2010. The evidence result suggests that Malaysia and Singapor's stock price and exchange rate are positively related. But Hong Kong's stock price is negatively related to exchange rate.

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.

Esta dissertação analisa a questão da seleção de modelos GARCH multivariados em termos da perfomance de previsão da matriz de covariância condicional. A aplicação empírica é realizada com 7 retornos de índices de ações envolvendo um conjunto de 34 especificações de modelos para os quais computamos as previsões da variância condicional um passo a frente para uma amostra com 60 observações para cada especificação dos modelos GARCH multivariados. A comparação entre os modelos é baseada no procedimento Model Confidence Set (MCS) avaliado através de duas funções perdas robustas a proxies de volatilidade imperfeitas. O MCS é um procedimento que permite comparar vários modelos simultaneamente em termos de sua habilidade preditiva e determinar um conjunto de modelos estatisticamente semelhantes em termos de previsão, dado um nível de confiança. / This paper considers the question of the selection of multivariate GARCH models in terms of covariance matrix forecasting. In the empirical application we consider 7 series of returns and compare a set of 34 model specifications based on one-step-ahead conditional variance forecasts over a sample with 60 observations. The comparison between models is performed with the Model Confidence Set (MCS) procedure evaluated using two loss functions that are robust against imperfect volatility proxies. The MCS is a procedure that allows both a multiple model comparison in terms of forecasting accuracy and the determination of a model set composed of statistically equivalent models, under a confidence level.

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.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The tight integration of world markets has enhanced the effects of financial crises. The financial crisis of 2007/2008, which started in the U.S. and then expanded to the rest of the world, had severe impact on virtually every market in the world and can be compared to the Great Depression occurred in 1929. This event again opened discussions about the financial crisis and its impact on various financial markets in the world. Investors have questioned the foundations upon which their decisions were founded on the risk of investing in stocks and the benefits of global diversification (BARTRAM AND BODNAR, 2009). Given this context, the aim of this study is to investigate the impacts of the capital markets of the United States in Latin American stock markets due to the crisis of 2007/2008. The empirical study on the effects of financial crises in capital markets in Latin America is divided into three parts: impacts on long-term relationship, short-term relationship and the transmission of volatility. The first part consists of the cointegration analysis of each of the Latin American markets with the United States, two by two. This analysis is performed using the cointegration test of Engle and Granger (1987). In the second phase of the study, we estimated models of vector autoregressive (VAR) and error correction (VEC) for each of the countries with the United States. In the third step, we employed the multivariate GARCH-BEKK model considering student-t distribution to model the transmission of volatility. All these models are estimated for the entire period and sub-periods before, during and after the crisis. Our results indicate that the relationships between the countries of Latin America and the United States changed due to the crisis that occurred in 2007/2008. Both the long-term relationship and the transmission in volatility between the countries of Latin America and the US were more evident in the period following the crisis than during it, revealing a greater integration between markets after the crisis. On the other hand, when we analyze the relationship between returns employing the VAR/VEC methodology, it is clear that during the crisis there was an increase in dependency lags in some markets, reducing this dependence on the period after the crisis. / A grande integração dos mercados mundiais potencializou os efeitos de crises financeiras. A crise financeira de 2007/2008, iniciada nos EUA e depois expandida para grande parte do mundo, teve severo impacto em praticamente todos os mercados do mundo, podendo ser comparada à Grande Depressão ocorrida em 1929. Esse evento abriu novamente as discussões a respeito das crises financeiras e suas repercussões nos diversos mercados financeiros do mundo. Os investidores têm questionado os fundamentos sobre os quais fundavam suas decisões sobre o risco do investimento em ações e os benefícios da diversificação global (BARTRAM e BODNAR, 2009). Tendo em vista este contexto, definiuse como objetivo geral do presente trabalho investigar os impactos do mercado de capitais dos Estados Unidos nos mercados latino-americanos devido a crise de 2007/2008. O estudo empírico a respeito do efeito das crises financeiras nos mercados de capitais da América Latina está dividido em três partes: impactos no relacionamento de longo prazo, no relacionamento de curto prazo e na transmissão da volatilidade. A primeira parte é composta pela análise de cointegração de cada um dos mercados latino-americanos com os Estados Unidos, dois a dois. Esta análise é realizada utilizando o teste de cointegração de Engle e Granger (1987). No segundo momento do estudo, são estimados modelos de vetor autoregressivo (VAR) e de correção de erro (VEC) de cada um dos países com os Estados Unidos. No terceiro passo é empregado o modelo BEKK de GARCH multivariado considerando a distribuição t-student para modelar a transmissão das volatilidades. Todos esses modelos são estimados para o período completo e os subperíodos antes, durante e depois da crise. Os resultados do estudo permitem inferir que houve mudança dos relacionamentos entre os países da América Latina e os Estados Unidos em função da crise ocorrida em 2007/2008. Tanto o relacionamento de longo prazo quanto a transmissão na volatilidade entre os países da América Latina tiveram uma resposta mais evidente no período após a crise do que durante esta, revelando uma maior integração entre mercados após a crise. Na análise do relacionamento entre retornos com a utilização do VAR e do VEC, por outro lado, percebe-se que durante a crise houve um aumento nas defasagens de dependência em alguns mercados, reduzindo esta dependência no período posterior à crise.