<p>The main goal of this work is to explore the effects of time-varying extreme jump tail dependencies in asset markets. Consequently, a lot of attention has been devoted to understand the extremal tail dependencies between of assets. As pointed by Hansen (2013), the estimation of tail risks dependence is a challenging task and their implications in several sectors of the economy are of great importance. One of the principal challenges is to provide a measure systemic risks that is, in principle, statistically tractable and has an economic meaning. Therefore, there is a need of a standardize dependence measures or at least to provide a methodology that can capture the complexity behind global distress in the economy. These measures should be able to explain not only the dynamics of the most recent financial crisis but also the prior events of distress in the world economy, which is the motivation of this paper. In order to explore the tail dependencies I exploit the information embedded in option prices and intra-daily high frequency data. </p><p>The first chapter, a co-authored work with Andrew Patton, proposes a new class of dynamic copula models for daily asset returns that exploits information from high frequency (intra-daily) data. We augment the generalized autoregressive score (GAS) model of Creal, et al. (2013) with high frequency measures such as realized correlation to obtain a "GRAS" model. We find that the inclusion of realized measures significantly improves the in-sample fit of dynamic copula models across a range of U.S. equity returns. Moreover, we find that out-of-sample density forecasts from our GRAS models are superior to those from simpler models. Finally, we consider a simple portfolio choice problem to illustrate the economic gains from exploiting high frequency data for modeling dynamic dependence.</p><p>In the second chapter using information from option prices I construct two new measures of dependence between assets and industries, the Jump Tail Implied Correlation and the Tail Correlation Risk Premia. The main contribution in this chapter is the construction of a systemic risk factor from daily financial measures using a quantile-regression-based methodology. In this direction, I fill the existing gap between downturns in the financial sector and the real economy. I find that this new index performs well to forecast in-sample and out-of-sample quarterly macroeconomic shocks. In addition, I analyze whether the tail risk of the correlation may be priced. I find that for the S&P500 and its sectors there is an ex ante premium to hedge against systemic risks and changes in the aggregate market correlation. Moreover, I provide evidence that the tails of the implied correlation have remarkable predictive power for future stock market returns.</p> / Dissertation

Deregulation of the energy market and surging trading activities have made the energy markets even more volatile in recent years. Under such circumstances, it becomes increasingly important to assess the probability of rare and extreme price movement in the risk management of energy futures. Similar to other financial time series, energy futures exhibit time varying volatility and fat tails. An appropriate risk measurement of energy futures should be able to capture these two features of the returns. In the first portion of this dissertation, we use the conditional Extreme Value Theory model to estimate Value-at-Risk (VaR) and Expected Shortfall (ES) for long and short trading positions in the energy markets. The statistical tests on the backtests show that this approach provides a significant improvement over the widely used Normal distribution based VaR and ES models. In the second portion of this dissertation, we extend our analysis from a single security to a portfolio of energy futures. In recent years, commodity futures have gained tremendous popularity as many investors believe they provide much needed diversification to their portfolios. In order to properly account for any diversification benefits, we employ a time-varying conditional bivariate copula approach to model the dependence structure between energy futures. In contrast to previous studies on the same subject, we introduce fundamental supply and demand factors into the copula models to study the dependence structure between energy futures. We find that energy futures are more likely to move together during down markets than up markets. In the third part of this dissertation, we extend our study of bivariate copula models to multivariate copula theory. We employ a pair-copula approach to estimate VaR and ES of a portfolio consisting of energy futures, the S&P 500 index and the US Dollar index. Our empirical results show that although the pair copula approach does not offer any added advantage in VaR and ES estimation over a long backtest horizon, it provides much more accurate estimates of risk during the period of high co-dependence among assets after the recent financial crisis.

Learning from data, especially ‘Big Data’, is becoming increasingly popular under names such as Data Mining, Data Science, Machine Learning, Statistical Learning and High Dimensional Data Analysis. In this dissertation we propose a new related field, which we call ‘United Nonparametric Data Science’ - applied statistics with “just in time” theory. It integrates the practice of traditional and novel statistical methods for nonparametric exploratory data modeling, and it is applicable to teaching introductory statistics courses that are closer to modern frontiers of scientific research. Our framework includes small data analysis (combining traditional and modern nonparametric statistical inference), big and high dimensional data analysis (by statistical modeling methods that extend our unified framework for small data analysis). The first part of the dissertation (Chapters 2 and 3) has been oriented by the goal of developing a new theoretical foundation to unify many cultures of statistical science and statistical learning methods using mid-distribution function, custom made orthonormal score function, comparison density, copula density, LP moments and comoments. It is also examined how this elegant theory yields solution to many important applied problems. In the second part (Chapter 4) we extend the traditional empirical likelihood (EL), a versatile tool for nonparametric inference, in the high dimensional context. We introduce a modified version of the EL method that is computationally simpler and applicable to a large class of “large p small n” problems, allowing p to grow faster than n. This is an important step in generalizing the EL in high dimensions beyond the p ≤ n threshold where the standard EL and its existing variants fail. We also present detailed theoretical study of the proposed method.

O aumento dos fluxos globais comerciais e financeiros, a partir da década de 90, e as diversas crises ocorridas até o atual período fizeram da avaliação de contágio um tema extremamente relevante, tanto para investidores quanto para formuladores de política. Nesse sentido, a presente dissertação tem como objetivo testar a hipótese de contágio financeiro para os mercados de Brasil, Inglaterra e Espanha em face à última crise americana de 2008. Para tanto, desenvolveu-se o artigo que integra o Capítulo 2 - a espinha dorsal deste trabalho - com dados diários dos retornos dos índices de Jan/2004 a Jun/2011. No âmbito da metodologia de cópulas, adotou-se uma estratégia empírica com base em duas etapas: i) a estimativa não paramétrica de cópulas, via kernel, utilizando o método desenvolvido em Fermanian et al. (2002) e a avaliação através de uma abordagem de bootstrap, sobre a ocorrência de um aumento significativo nas medidas de dependência delas extraídas; ii) testes sobre a igualdade entre cópulas empíricas, conforme proposto por Remillard e Scaillet (2009), a fim de verificar se houve mudança na estrutura de dependência a partir da crise. Os resultados obtidos nas duas etapas da estratégia empírica são semelhantes e sugerem a existência de contágio financeiro para os países analisados no período estudado. / The increase in global trade and financial flows since the 90’s, and the various crises in the current period until these days made contagion an extremely important issue for both investors and policy makers. Accordingly, this dissertation aims to test the hypothesis of financial contagion between USA and markets in Brazil, England and Spain in the face of the last USA crisis of 2008. To this end, we produce the article in Chapter 2 - the backbone of this work - with daily data of index-returns from Jan/2004 to Jun/2011. Under the scope of copula methodology, we addopt an empirical strategy based on two steps: i) estimating nonparametric copulas via kernel, using the method developed in Fermanian et al. (2002) and assessing through a bootstrap approach whether a significant change in dependence measures extracts thereof, ii) testing whether two empirical estimated copulas are the same, as proposed by Remillard e Scaillet (2009), to check again whether dependence structures change with crisis. The results obtained in these two steps of the empirical strategy are similar and suggest the existence of financial contagion between the countries analysed in the studied period.

vi Abstract Proper understanding of the dependence between assets is a crucial ingredient for a number of portfolio and risk management tasks. While the research in this area has been lively for decades, the recent financial crisis of 2007-2008 reminded us that we might not understand the dependence properly. This crisis served as catalyst for boosting the demand for models capturing the dependence structures. Reminded by this urgent call, literature is responding by moving to nonlinear de- pendence models resembling the dependence structures observed in the data. In my dissertation, I contribute to this surge with three papers in financial econo- metrics, focusing on nonlinear dependence in financial time series from different perspectives. I propose a new empirical model which allows capturing and forecasting the conditional time-varying joint distribution of the oil - stocks pair accurately. Em- ploying a recently proposed conditional diversification benefits measure that con- siders higher-order moments and nonlinear dependence from tail events, I docu- ment decreasing benefits from diversification over the past ten years. The diver- sification benefits implied by my empirical model are, moreover, strongly varied over time. These findings have important implications for asset allocation, as the benefits of...

Notre objectif de ce travail est d’étudier l’efficience du marché financier tunisien avant et après la révolution de Jasmin de 2011 et de déterminer les facteurs macroéconomiques et financiers qui influencent le score d’efficience de ce marché. Notre méthodologie consiste à utiliser dans un premier temps le modèle GARCH multivarié pour estimer le coefficient de corrélation entre les rendements du marché et ceux des différentes banques et le coefficient Béta. Comme ce modèle suppose des résidus qui suivent la loi normale multivariée qui est une hypothèse non vérifiée dans la pratique, nous allons utiliser dans un deuxième temps la théorie des copules pour donner une plus grande souplesse dans la modélisation des données multivariées. Les facteurs les plus influents sont déterminés en utilisant le modèle de régression linéaire,le modèle de données de Panel et le modèle TOBIT. Les résultats empiriques montrent que le marché tunisien n’est pas efficient ni avant ni après la révolution. Beaucoup d’actions sont proposées pour améliorer le degré d’efficience de ce marché. / Our objective of this work is to study the efficiency of the Tunisian financial market before and after the Jasmin revolution of 2011 and identify macro-economic and financial factors that influence the efficiency score of this market. Our methodology is to use at first multivariate GARCH model to estimate the correlation between market returns and those of individual banks and the Beta coefficient. As this model assumes the residues that follow the multivariate normal law is untested in practice, we used in a second step the copula theory to provide more flexibility in modeling multivariate data. The most influential factors are determined using the linear regression model, the panel data model and TOBIT model. The empirical results show that the Tunisian market is not efficient either before or after the revolution. Many actions are proposed to improve the degree of efficiency of this market.

A mensuração do risco de um investimento é uma das mais importantes etapas para a tomada de decisão de um investidor. Em virtude disto, este trabalho comparou três métodos de estimação (tradicional, através da analise univariada dos retornos do portfólio; cópulas estáticas e cópulas dinâmicas) de duas medidas de risco: Value at Risk (VaR) e Expected Shortfall (ES). Tais medidas foram estimadas para o portfólio composto pelos índices BOVESPA e S&P500 no período de janeiro de 1998 a maio de 2012. Para as modelagens univariadas, incluindo as marginais das cópulas, foram comparados os modelos GARCH e EGARCH. Para cada modelo univariado, utilizamos as cópulas Normal, t-Student, Gumbel rotacionada e Joe-Clayton simetrizada, com isso totalizando 36 modelos comparados. Nas comparações do VaR e ES foram utilizados, respectivamente, o teste de Chritoffersen e o teste de Mcneil e Frey. Os principais resultados encontrados foram a superioridade de modelos que supõem erros com distribuição t-Student, assim como a identificação de mudança no comportamento dos parâmetros dinâmicos nos períodos de crise. / Measuring the risk of an investment is one of the most important steps in an investor's decision-making. With this in light, this study compared three estimation methods (traditional; by univariate analysis of portfolio returns; dynamic copulas and static copulas), of two risk measurements: Value at Risk (VaR) and Expected Shortfall (ES). Such estimated measures are performed for a portfolio composed by the BOVESPA and S&P500 indexes, ranging from January 1998 to May 2012. For univariate modelling (including copulas marginals), the GARCH and EGARCH models were compared,. Regarding copulas, we use Normal, t-Student, rotated Gumbel and symmetric Joe-Clayton, leading to a total of 36 models being compared. For the comparison of VaR and ES were used, respectively, the Christoffersen test, and the Mcneil and Frey test. The main results found were the superiority of models assuming the t-Student distributed errors, as well as the identification of a change in the behaviour of dynamic parameters in periods of crisis.

abstract: A quantitative analysis of a system that has a complex reliability structure always involves considerable challenges. This dissertation mainly addresses uncertainty in- herent in complicated reliability structures that may cause unexpected and undesired results. The reliability structure uncertainty cannot be handled by the traditional relia- bility analysis tools such as Fault Tree and Reliability Block Diagram due to their deterministic Boolean logic. Therefore, I employ Bayesian network that provides a flexible modeling method for building a multivariate distribution. By representing a system reliability structure as a joint distribution, the uncertainty and correlations existing between system’s elements can effectively be modeled in a probabilistic man- ner. This dissertation focuses on analyzing system reliability for the entire system life cycle, particularly, production stage and early design stages. In production stage, the research investigates a system that is continuously mon- itored by on-board sensors. With modeling the complex reliability structure by Bayesian network integrated with various stochastic processes, I propose several methodologies that evaluate system reliability on real-time basis and optimize main- tenance schedules. In early design stages, the research aims to predict system reliability based on the current system design and to improve the design if necessary. The three main challenges in this research are: 1) the lack of field failure data, 2) the complex reliability structure and 3) how to effectively improve the design. To tackle the difficulties, I present several modeling approaches using Bayesian inference and nonparametric Bayesian network where the system is explicitly analyzed through the sensitivity analysis. In addition, this modeling approach is enhanced by incorporating a temporal dimension. However, the nonparametric Bayesian network approach generally accompanies with high computational efforts, especially, when a complex and large system is modeled. To alleviate this computational burden, I also suggest to building a surrogate model with quantile regression. In summary, this dissertation studies and explores the use of Bayesian network in analyzing complex systems. All proposed methodologies are demonstrated by case studies. / Dissertation/Thesis / Doctoral Dissertation Industrial Engineering 2018

O aumento dos fluxos globais comerciais e financeiros, a partir da década de 90, e as diversas crises ocorridas até o atual período fizeram da avaliação de contágio um tema extremamente relevante, tanto para investidores quanto para formuladores de política. Nesse sentido, a presente dissertação tem como objetivo testar a hipótese de contágio financeiro para os mercados de Brasil, Inglaterra e Espanha em face à última crise americana de 2008. Para tanto, desenvolveu-se o artigo que integra o Capítulo 2 - a espinha dorsal deste trabalho - com dados diários dos retornos dos índices de Jan/2004 a Jun/2011. No âmbito da metodologia de cópulas, adotou-se uma estratégia empírica com base em duas etapas: i) a estimativa não paramétrica de cópulas, via kernel, utilizando o método desenvolvido em Fermanian et al. (2002) e a avaliação através de uma abordagem de bootstrap, sobre a ocorrência de um aumento significativo nas medidas de dependência delas extraídas; ii) testes sobre a igualdade entre cópulas empíricas, conforme proposto por Remillard e Scaillet (2009), a fim de verificar se houve mudança na estrutura de dependência a partir da crise. Os resultados obtidos nas duas etapas da estratégia empírica são semelhantes e sugerem a existência de contágio financeiro para os países analisados no período estudado. / The increase in global trade and financial flows since the 90’s, and the various crises in the current period until these days made contagion an extremely important issue for both investors and policy makers. Accordingly, this dissertation aims to test the hypothesis of financial contagion between USA and markets in Brazil, England and Spain in the face of the last USA crisis of 2008. To this end, we produce the article in Chapter 2 - the backbone of this work - with daily data of index-returns from Jan/2004 to Jun/2011. Under the scope of copula methodology, we addopt an empirical strategy based on two steps: i) estimating nonparametric copulas via kernel, using the method developed in Fermanian et al. (2002) and assessing through a bootstrap approach whether a significant change in dependence measures extracts thereof, ii) testing whether two empirical estimated copulas are the same, as proposed by Remillard e Scaillet (2009), to check again whether dependence structures change with crisis. The results obtained in these two steps of the empirical strategy are similar and suggest the existence of financial contagion between the countries analysed in the studied period.

A mensuração do risco de um investimento é uma das mais importantes etapas para a tomada de decisão de um investidor. Em virtude disto, este trabalho comparou três métodos de estimação (tradicional, através da analise univariada dos retornos do portfólio; cópulas estáticas e cópulas dinâmicas) de duas medidas de risco: Value at Risk (VaR) e Expected Shortfall (ES). Tais medidas foram estimadas para o portfólio composto pelos índices BOVESPA e S&P500 no período de janeiro de 1998 a maio de 2012. Para as modelagens univariadas, incluindo as marginais das cópulas, foram comparados os modelos GARCH e EGARCH. Para cada modelo univariado, utilizamos as cópulas Normal, t-Student, Gumbel rotacionada e Joe-Clayton simetrizada, com isso totalizando 36 modelos comparados. Nas comparações do VaR e ES foram utilizados, respectivamente, o teste de Chritoffersen e o teste de Mcneil e Frey. Os principais resultados encontrados foram a superioridade de modelos que supõem erros com distribuição t-Student, assim como a identificação de mudança no comportamento dos parâmetros dinâmicos nos períodos de crise. / Measuring the risk of an investment is one of the most important steps in an investor's decision-making. With this in light, this study compared three estimation methods (traditional; by univariate analysis of portfolio returns; dynamic copulas and static copulas), of two risk measurements: Value at Risk (VaR) and Expected Shortfall (ES). Such estimated measures are performed for a portfolio composed by the BOVESPA and S&P500 indexes, ranging from January 1998 to May 2012. For univariate modelling (including copulas marginals), the GARCH and EGARCH models were compared,. Regarding copulas, we use Normal, t-Student, rotated Gumbel and symmetric Joe-Clayton, leading to a total of 36 models being compared. For the comparison of VaR and ES were used, respectively, the Christoffersen test, and the Mcneil and Frey test. The main results found were the superiority of models assuming the t-Student distributed errors, as well as the identification of a change in the behaviour of dynamic parameters in periods of crisis.