In the context of the guarantee liability valuation, the sophisticated fund-of-funds structure, of some Canadian segregated fund products, often requires us to model multiple market indices simultaneously in order to benchmark the return of the underlying fund. In this thesis, we apply multivariate GARCH models with Gaussian and non-Gaussian noise to project the future investment scenarios of the fund. We further conduct a simulation study to investigate the difference, among the proposed multivariate models, in the valuation of the Guaranteed Minimum Maturity Benefit (GMMB) option. Based on the pre-data analysis, the proposed multivariate GARCH models are data driven. The goodness-of-fit for the models is evaluated through formal statistical tests from univariate and multivariate perspectives. The estimation and associated practical issues are discussed in details. The impact from the innovation distributions is addressed. More importantly, we demonstrate an actuarial approach to manage the guarantee liability for complex segregated fund products.

In the context of the guarantee liability valuation, the sophisticated fund-of-funds structure, of some Canadian segregated fund products, often requires us to model multiple market indices simultaneously in order to benchmark the return of the underlying fund. In this thesis, we apply multivariate GARCH models with Gaussian and non-Gaussian noise to project the future investment scenarios of the fund. We further conduct a simulation study to investigate the difference, among the proposed multivariate models, in the valuation of the Guaranteed Minimum Maturity Benefit (GMMB) option. Based on the pre-data analysis, the proposed multivariate GARCH models are data driven. The goodness-of-fit for the models is evaluated through formal statistical tests from univariate and multivariate perspectives. The estimation and associated practical issues are discussed in details. The impact from the innovation distributions is addressed. More importantly, we demonstrate an actuarial approach to manage the guarantee liability for complex segregated fund products.

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)

The generalization from the univariate volatility model into a multivariate approach opens up a variety of modeling possibilities. This study aims to examine the performance of the two multivariate GARCH models BEKK and DCC, applied on ten years exchange rates data. Estimations and forecasts of the covariance matrix are made for the EUR/SEK and USD/SEK, whereby the  used in a practical application: 1-day and 10-day ahead historical simulated Value-at-Risk predictions for two theoretical portfolios, one equally weighted and one hedged, consisting of the two exchange rates. An univariate GARCH(1,1) approach is included in the Vale-at-Risk predictions to visualize the diversification effect in the portfolio. The conditional correlation forecasts are evaluated using three measures, OLS-regression, MAE and RMSE, based on an one year evaluation period of intraday data. The Value-at-Risk estimates are evaluated with the backtesting method introduced by Kupiec (1995). The results indicate that the BEKK model performs relatively better than the DCC model, and both these models perform better than the univariate GARCH(1,1) model.

Over the last twenty years or so the Dynamic Volatility literature has produced a wealth of univariate and multivariate GARCH type models. While the univariate models have been relatively successful in empirical studies, they suffer from a number ofweaknesses, such as unverifiable parameter restrictions, existence of moment conditions and the retention of Normality. These problems are naturally more acute in the multivariate GARCH type models, which in addition have the problem of overparameterization. This dissertation uses the Student's t distribution and follows the Probabilistic Reduction (PR) methodology to modify and extend the univariate and multivariate volatility models viewed as alternative to the GARCH models. Its most important advantage is that it gives rise to internally consistent statistical models that do not require ad hoc parameter restrictions unlike the GARCH formulations. Chapters 1 and 2 provide an overview of my dissertation and recent developments in the volatility literature. In Chapter 3 we provide an empirical illustration of the PR approach for modeling univariate volatility. Estimation results suggest that the Student's t AR model is a parsimonious and statistically adequate representation of exchange rate returns and Dow Jones returns data. Econometric modeling based on the Student's t distribution introduces an additional variable - the degree of freedom parameter. In Chapter 4 we focus on two questions relating to the `degree of freedom' parameter. A simulation study is used to examine:(i) the ability of the kurtosis coefficient to accurately capture the implied degrees of freedom, and (ii) the ability of Student's t GARCH model to estimate the true degree of freedom parameter accurately. Simulation results reveal that the kurtosis coefficient and the Student's t GARCH model (Bollerslev, 1987) provide biased and inconsistent estimators of the degree of freedom parameter. Chapter 5 develops the Students' t Dynamic Linear Regression (DLR) }model which allows us to explain univariate volatility in terms of: (i) volatility in the past history of the series itself and (ii) volatility in other relevant exogenous variables. Empirical results of this chapter suggest that the Student's t DLR model provides a promising way to model volatility. The main advantage of this model is that it is defined in terms of observable random variables and their lags, and not the errors as is the case with the GARCH models. This makes the inclusion of relevant exogenous variables a natural part of the model set up. In Chapter 6 we propose the Student's t VAR model which deals effectively with several key issues raised in the multivariate volatility literature. In particular, it ensures positive definiteness of the variance-covariance matrix without requiring any unrealistic coefficient restrictions and provides a parsimonious description of the conditional variance-covariance matrix by jointly modeling the conditional mean and variance functions. / Ph. D.

In this thesis we study the regional and global linkages as evidence of markets integration of the stock markets in Frankfurt, Amsterdam, Prague the U.S. and the dynamics of volatility transmission of related foreign exchange rates using multivariate GARCH approach. For each of the model classes, a theoretical review, basic properties and estimation procedure are provided. We illustrate approach by applying the models to daily market data. Our two main aims are discussing and report the existence of regional and global stock markets linkages and provide comparison of such multivariate GARCH models on the data sample. We find out that the estimated time-varying conditional correlations indicate limited integration among the markets which implies that investors can benefit from the risk reduction by investigating in the different stock markets especially during the crisis.

Since the introduction univariate GARCH models number of available models have grown rapidly and has been extended to the multivariate area. This paper compares three different multivariate GARCH models and they are evaluated using out of sample Value at Risk of dif- ferent portfolios. Sector portfolios are used with different market capitalization. The models compared are the DCC,CCC and the GO-Garch model. The forecast horizon is 1-day, 5-day and 10-day ahead forecast of the estimated VaR limit. The DCC performs best with regards to both conditional anc unconditional violations of the VaR estimates.

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.