The present paper develops a procedure based on multivariate copulas for simulating multivariate non-normal data that satisfies a pre-specified covariance matrix. The covariance matrix used, can comply with a specific moment structure form (e.g., a factor analysis or a general SEM model). So the method is particularly useful for Monte Carlo evaluation of SEM models in the context of non-normal data. The new procedure for non-normal data simulation is theoretically described and also implemented on the widely used R environment. The quality of the method is assessed by performing Monte Carlo simulations. Within this context a one-sample test on the observed VC-matrix is involved. This test is robust against normality violations. This test is defined through a particular SEM setting. Finally, an example for Monte Carlo evaluation of SEM modeling of non-normal data using this method is presented. (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics

Dans cette thèse, nous examinons les apports importants de la modélisation de la dépendance par la théorie des copules dans le cadre des problématiques liées à la gestion des portefeuilles financiers et des produits structurés de crédits.La première partie de cette thèse est consacrée à la gestion des portefeuilles financiers. Nous étudions en premier lieu la relation qui peut s'établir entre le niveau de diversification du portefeuille et le choix de la copule ayant décrit au mieux la structure de dépendance. L'objectif est de pouvoir identifier une caractéristique dans les portefeuilles permettant une sélection plus simple de la copule appropriée. Dans un deuxième chapitre, nous proposons d'étudier l'impact d'une mauvaise spécification du modèle de copule sur les estimations des mesures de risque conventionnelles telles la Value-at-Risk et l'Expected-Shortfall. L'idée est de vérifier l'utilité de développer ces estimations sous l'angle du vrai modèle copule. Dans un troisième chapitre, nous étudions l'impact d'une mauvaise spécification du modèle copule dans le cadre d'un problème d'allocation optimale de portefeuilles. L'objectif principal vise surtout à identifier la sensibilité des investisseurs, en fonction de leurs degrés d'aversion aux risques (pertes), pour l'une au l'autre des composante du modèle copule. Nous proposons ainsi d'établir une passerelle entre les enseignements des théories de la finance comportementale et la modélisation de la dépendance par la théorie des copules.La deuxième partie de la thèse porte sur les produits structurés de crédit. Nous étudions, dans un premier chapitre, l'apport d'un modèle actuariel, utilisant les fonctions copules dans la modélisation de la structure de dépendance entre les temps de défauts, dans le cadre du processus d'estimation des mesures de risque. Enfin, dans un dernier chapitre nous revisitons la notion du « Diversity Score », développée par l'agence de notation Moody's dans l'objectif d'assigner la qualité de produits structurés de crédit en terme de diversification. Nous discutons de l'analogie de cette mesure avec celle de l'approche copule, et nous démontrons son adéquation avec quelques familles de fonctions copules. / In this thesis, we examine one key topic related to copula theory contributions to the financial portfolio management theory and to the study of structured credit products.The first part of this thesis deals with financial portfolio management. We first discuss the relationship between portfolio diversification and the choice of the copula that better describes the dependence structure. The goal is to identify one feature of portfolios making straightforward the process of the appropriate copula selection. In the second chapter, we propose to study the impact of copula model misspecification, on conventional risk measures estimates as for the example of Value-at-Risk and Expected-Shortfall. The idea is to check the validity of developing these estimates under the true copula model. In a third chapter, we apply such approach to optimal portfolio allocation problem. The main objective is to identify investor's sensitivity, depending on their risk (or loss) aversion, to one of the component of the copula model. Thus, we propose one possible linkage between the behavioral finance theory and the copula functions framework.The second part of the thesis focuses on structured credit products. In a first chapter, we study the contribution of an actuarial model, using copulas functions in modeling the dependence structure between times of defaults, in the process of risk measures estimates. Finally, in a last chapter we re-examine the “Diversity Score” concept, developed by the Moody's rating agency to assign the quality of structured credit portfolio in terms of diversification. We discuss the analogy of this measure with that of the copula approach, and demonstrate its adequacy with some copula functions families.

Este trabalho testa, através da metodologia de cópulas, a hipótese de contágio financeiro entre ações brasileiras e índices de mercado dos países que deram origem às crises do Terror em 2001, da Argentina em 2001, dos Subpprimes em 2007 e do Débito Soberano Europeu em 2009. Além disso, ainda é feita uma análise dos setores econômicos que mais foram afetados por cada crise. Os testes da crise do Terror apresentaram evidências de contágio do SP500 para 24 ações brasileiras, afetando, principalmente os setores ligado à indústria e à energia. As crises da Argentina e do Débito Soberano Europeu apresentaram evidências de contágio dos índices Merval e Athex para apenas 3 empresas. A crise dos Subprimes apresentou evidências de contágio do SP500 para 35 empresas brasileiras, sendo a maioria ligada aos setores financeiros, de energia e industrial. 7 ações foram afetadas pelas duas crises norteamericanas. Os resultados reforçam a importância da análise de contágio em cada empresa individual, ao invés de utilizar o índice do mercado brasileiro como um todo. / This paper tests, through the copulas methodology, the hypothesis of financial contagion between the individual Brazilian stocks and the market indices of the countries where the crises were originated. The crises analyzed are the Terror crisis in 2001, the Argentina’s crisis in 2001, the Subprime crisis in 2007 and the Sovereign Debt crisis in 2009. In addition to this, the Brazilian economic sectors are examined in order to find out which were most affected by each crisis. The tests of the Terror crisis presented evidence of SP500 contagion to 24 Brazilian stocks, affecting, mainly, sectors related to industry and energy. The Argentina’s crisis and the European Sovereign Debt crisis presented contagion’s evidence of the Merval and Athex indices for only 3 Brazilian companies. The Subprimes crisis presented evidence of SP500 contagion for 35 Brazilian companies, mostly related to the financial, energy and industrial sectors. 7 Brazilian stocks were affected by both American crises. The results reinforce the importance of contagion analysis in each individual company, rather than using the Brazilian market index.

Os mercados financeiros são de extrema relevância para as diversas economias do mundo. Sua efetividade na atração de capitais e investimentos é notória. Atualmente, o fluxo financeiro entre os diversos países é muito intenso, devido ao fenômeno da globalização. Tal situação provoca transmissão de crises financeiras entre diferentes países. Neste contexto, a avaliação de contágio financeiro torna-se um tema bastante relevante. A presente dissertação almejou verificar se houve contágio financeiro da crise americana de 2008 sobre os países do BRIC (Brasil, Rússia, Índia e China). Para tanto, foram utilizadas duas metodologias distintas. Uma delas, devido a Fermanian et al. (2002), foi empregada para estimação não paramétrica das cópulas via kernel. Assim, pode-se averiguar se houve aumento significativo nas medidas de dependência. A outra, desenvolvida por Remillard e Scaillet (2009), é um teste de comparação entre duas cópulas empíricas que investiga se houve mudança na estrutura de dependência no período de crise. Os dois procedimentos metodológicos indicaram a ocorrência de contágio da crise americana de 2008 sobre todos os países do BRIC. / Financial markets are extremely relevant to the world's diverse economies. Its effectiveness in attracting capital and investments is notorious. Currently, the financial flow between the various countries is very intense, due to the phenomenon of globalization. This situation leads to the transmission of financial crises between different countries. In this context, the evaluation of financial contagion becomes a very relevant issue. The present dissertation aimed to verify if there was financial contagion of the 2008 US crisis on the BRIC countries (Brazil, Russia, India and China). For that, two different methodologies were used. One of them, due to Fermanian et al. (2002), was used for non-parametric estimation of copula via kernel. Thus, it can be verified if there was a significant increase in the measures of dependence. The other, developed by Remillard and Scaillet (2009), is a test of comparison between two empirical copulas that investigates if there was a change in the dependency structure in the crisis period. The two methodological procedures indicated the occurrence of contagion of the American crisis of 2008 on all BRIC countries.

Este trabalho testa, através da metodologia de cópulas, a hipótese de contágio financeiro entre ações brasileiras e índices de mercado dos países que deram origem às crises do Terror em 2001, da Argentina em 2001, dos Subpprimes em 2007 e do Débito Soberano Europeu em 2009. Além disso, ainda é feita uma análise dos setores econômicos que mais foram afetados por cada crise. Os testes da crise do Terror apresentaram evidências de contágio do SP500 para 24 ações brasileiras, afetando, principalmente os setores ligado à indústria e à energia. As crises da Argentina e do Débito Soberano Europeu apresentaram evidências de contágio dos índices Merval e Athex para apenas 3 empresas. A crise dos Subprimes apresentou evidências de contágio do SP500 para 35 empresas brasileiras, sendo a maioria ligada aos setores financeiros, de energia e industrial. 7 ações foram afetadas pelas duas crises norteamericanas. Os resultados reforçam a importância da análise de contágio em cada empresa individual, ao invés de utilizar o índice do mercado brasileiro como um todo. / This paper tests, through the copulas methodology, the hypothesis of financial contagion between the individual Brazilian stocks and the market indices of the countries where the crises were originated. The crises analyzed are the Terror crisis in 2001, the Argentina’s crisis in 2001, the Subprime crisis in 2007 and the Sovereign Debt crisis in 2009. In addition to this, the Brazilian economic sectors are examined in order to find out which were most affected by each crisis. The tests of the Terror crisis presented evidence of SP500 contagion to 24 Brazilian stocks, affecting, mainly, sectors related to industry and energy. The Argentina’s crisis and the European Sovereign Debt crisis presented contagion’s evidence of the Merval and Athex indices for only 3 Brazilian companies. The Subprimes crisis presented evidence of SP500 contagion for 35 Brazilian companies, mostly related to the financial, energy and industrial sectors. 7 Brazilian stocks were affected by both American crises. The results reinforce the importance of contagion analysis in each individual company, rather than using the Brazilian market index.

Os mercados financeiros são de extrema relevância para as diversas economias do mundo. Sua efetividade na atração de capitais e investimentos é notória. Atualmente, o fluxo financeiro entre os diversos países é muito intenso, devido ao fenômeno da globalização. Tal situação provoca transmissão de crises financeiras entre diferentes países. Neste contexto, a avaliação de contágio financeiro torna-se um tema bastante relevante. A presente dissertação almejou verificar se houve contágio financeiro da crise americana de 2008 sobre os países do BRIC (Brasil, Rússia, Índia e China). Para tanto, foram utilizadas duas metodologias distintas. Uma delas, devido a Fermanian et al. (2002), foi empregada para estimação não paramétrica das cópulas via kernel. Assim, pode-se averiguar se houve aumento significativo nas medidas de dependência. A outra, desenvolvida por Remillard e Scaillet (2009), é um teste de comparação entre duas cópulas empíricas que investiga se houve mudança na estrutura de dependência no período de crise. Os dois procedimentos metodológicos indicaram a ocorrência de contágio da crise americana de 2008 sobre todos os países do BRIC. / Financial markets are extremely relevant to the world's diverse economies. Its effectiveness in attracting capital and investments is notorious. Currently, the financial flow between the various countries is very intense, due to the phenomenon of globalization. This situation leads to the transmission of financial crises between different countries. In this context, the evaluation of financial contagion becomes a very relevant issue. The present dissertation aimed to verify if there was financial contagion of the 2008 US crisis on the BRIC countries (Brazil, Russia, India and China). For that, two different methodologies were used. One of them, due to Fermanian et al. (2002), was used for non-parametric estimation of copula via kernel. Thus, it can be verified if there was a significant increase in the measures of dependence. The other, developed by Remillard and Scaillet (2009), is a test of comparison between two empirical copulas that investigates if there was a change in the dependency structure in the crisis period. The two methodological procedures indicated the occurrence of contagion of the American crisis of 2008 on all BRIC countries.

Orientador: Mauricio Enrique Zevallos Herencia / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-13T23:05:02Z (GMT). No. of bitstreams: 1 Abbara_OmarMuhieddineFranco_M.pdf: 3046257 bytes, checksum: d44908ec7942d0684a67c6de5242a86c (MD5) Previous issue date: 2009 / Resumo: A modelagem multivariada de séries financeiras se constitui em um dos mais importantes e desafiadores problemas na área de econometria financeira. Um dos modelos populares nesta área é o modelo de cópulas, dada sua flexibilidade para construir funções de distribuição multivariadas que reproduzam dependências não lineares. Este trabalho está focado no estudo e aplicação de modelos de cópulas com dimensão maior que três, em problemas de interdependência, contágio e gerenciamento de risco. Primeiramente é realizada a modelagem bivariada de retornos de índices considerando os mercados de Estados Unidos, os principais mercados financeiros latino-americanos e europeus, utilizando copulas variando no tempo segundo a metodologia proposta por Patton(2006). Em seguida é proposta a especificação de um modelo de cópulas trivariado com parâmetros variando no tempo combinando as propostas de Patton (2006) e Aas et. al. (2009). Em terceiro lugar a análise de dependência e contagio entre os retornos estudados é feita através do uso de copulas condicionais. Esta análise, conjuntamente com a proposta do modelo trivariado de cópulas com parâmetros variando no tempo, constituem as principais contribuições metodológicas deste trabalho. Finalmente, cópulas tetravariadas são empregadas na análise de risco de ações negociadas no mercado à vista brasileiro / Abstract: Multivariate modelling of financial time series is one of the most important and challenging issue in financial econometrics. One of the most popular model in this subject is copula models, mainly because its flexible properties to construct multivariate distributions in which it is possible to reproduce nonlinear dependence. This work studies and applies copula models with dimension higher than two in issues of interdependence, contagion and risk management. At first it is fitted bivariate copula models with time-varying parameters proposed by Patton (2006) considering the north american stock markets and the most important markets of latin America and europe. After that it is proposed a trivariate copula model with time-varying parameter which combines the methodologies of Patton (2006) and Aas et. al. (2009). At third the analysis of dependence and contagion among returns under study is made through a conditional copula model. Both the analysis through a conditional copula and the trivariate copula model with time-varying parameters are the main methodological contributions of this work. Finally, 4-variate copula models are applied in risk management in brazilian stock market / Mestrado / Econometria Financeira / Mestre em Estatística

As relações de dependência entre variáveis aleatórias é um dos assuntos mais discutidos em probabilidade e estatística e a forma mais abrangente de estudar essas relações é por meio da distribuição conjunta. Nos últimos anos vem crescendo a utilização de cópulas para representar a estrutura de dependência entre variáveis aleatórias em uma distribuição multivariada. Contudo, ainda existe pouca literatura sobre cópulas quando as distribuições marginais são discretas. No presente trabalho será apresentada uma proposta não-paramétrica de estimação da distribuição conjunta bivariada de variáveis aleatórias discretas utilizando cópulas e polinômios de Bernstein. / The relations of dependence between random variables is one of the most discussed topics in probability and statistics and the best way to study these relationships is through the joint distribution. In the last years has increased the use of copulas to represent the dependence structure among random variables in a multivariate distribution. However, there is still little literature on copulas when the marginal distributions are discrete. In this work we present a non-parametric approach for the estimation of the bivariate joint distribution of discrete random variables using copulas and Bernstein polynomials.

In epidemiological studies, subjects with disease (prevalent cases) differ from newly diseased (incident cases). They tend to survive longer due to sampling bias, and related covariates will also be biased. Methods for regression analyses have recently been proposed to measure the potential effects of covariates on survival. The goal is to extend the dependence measure of Kent (1983), based on the information gain, in the context of length-biased sampling. In this regard, to estimate information gain and dependence measure for length-biased data, we propose two different methods namely kernel density estimation with a regression procedure and parametric copulas. We will assess the consistency for all proposed estimators. Algorithms detailing how to generate length-biased data, using kernel density estimation with regression procedure and parametric copulas approaches, are given. Finally, the performances of the estimated information gain and dependence measure, under length-biased sampling, are demonstrated through simulation studies.

This thesis includes four essays on risk assessment with financial econometrics models. The first chapter provides Monte Carlo evidence on the efficiency gains obtained in GARCH-base estimations of VaR and ES by incorporating dependence information through copulas and subsequently using full maximum likelihood (FML) estimates. First, individual returns series are considered; in this case, the efficiency gain stems from exploiting the relationship with another returns series using a copula model. Second, portfolio returns series obtained as a linear combination of returns series related with a copula model, are considered; in this case, the efficiency gain stems from using FML estimates instead of two-stage maximum likelihood estimates. Our results show that, in these situations, using copula models and FML leads to a substantial reduction in the mean squared error of the VaR and ES estimates (around 50\% when there is a medium degree of dependence between returns) and a notable improvement in the performance of backtesting procedures. Then, chapter 2 analyzes the impact of the COVID-19 pandemic on the conditional variance of stock returns. In this work, we look at this effect from a global perspective, employing series of major stock market and sector indices. We use the Hansen’s Skewed-t distribution with EGARCH extended to control for sudden changes in volatility. We oversee the COVID-19 effect on the VaR. Our results show that there is a significant sudden shift up in the return distribution variance post the announcement of the pandemic, which must be explained properly to obtain reliable measures for financial risk management. In chapter 3, we assess VaR and ES estimates assuming different models for standardised returns such as Cornish-Fisher and Gram-Charlier polynomial expansions, and well-known parametric densities such as normal, skewed Student-t family of Zhu and Galbraith (2010), and Johnson. This paper aims to check whether models based on polynomial expansions outperform the parametric ones. We carry out the model performance comparison in two stages. First, a backtesting analysis for VaR and ES, and second, using the loss function approach. Our backtesting results in our empirical exercise suggest that all distributions, but the normal, perform quite well in VaR and ES estimations. Regarding the loss function analysis, we conclude that the Cornish-Fisher expansion usually outperforms the others in VaR estimation, but Johnson distribution is the one that provides the best ES estimates in most cases. Although the differences among all distributions (excluding the normal) are not great. Finally, chapter 4 assess whether accounting for asymmetry and tail-dependence in returns distributions may help to identify more profitable investment strategies in asset portfolios. Three copula models are used to parameterize the multivariate distribution of returns: Gaussian, C-Vine and R-Vine copulas. Using data from equities and ETFs from the US market, we find evidence that, for portfolios of 48 constituents or less, the R-Vine copula is able to produce more profitable portfolios with respect to both, the C-Vine and Gaussian copulas. However, for portfolios of 100 assets, performance of R- and C-Vine copulas is quite similar, being both better than the Gaussian copula.