Due to the financial turmoil in recent years, risk management has become an important issue, investors would like to be fully-prepared to cope with financial crisis before it happen. This research uses the Fama and French three-factor and the U.S. Dollar Index (USDX) as an exchange rate variations indicator to capture the international relations. It constitutes a four-factor model to analyze the S&P100 stock returns changes, and we introduce the skewed-t distribution to simulate the distribution of stock returns and capture the characteristics of skewness and kurtosis. We use cluster analysis to cluster the sample companies by their risk characteristics. And then we observe the explanatory power of each risk factor. The study shows that the S&P100 stocks are subjected to the market premium, and the scale effect is smaller than others. ¡@¡@ At last, in accordance with the GARCH-Skewed-t model to simulate the average, variance, skewness and kurtosis of each cluster. We track the long-term performance of each parameter which are used to observe the unusual changes before financial crisis. The empirical results show that the skewness parameter has perfect warning for financial turmoil. The cluster with warning ability is affected by B/M ratio effect and exchange rate changes. Among the case, the cluster has the best early warning effect when it's influenced by the exchange rate indicator. It displays that by adding an exchange rate risk indicator into the multi-factor model, we will have a better clustering result. It means that the skewness parameter of cluster with influence of exchange rate indicator can be used to observe financial turmoil, which can in turns, be used as an early warning system to determine the occurrence of extreme events.

A modelagem da estrutura de dependência é de grande importância em todos os ramos da economia onde há incerteza. Ela é um elemento crucial na análise de risco e para a tomada de decisão sob incerteza. As cópulas oferecem aos agentes que se deparam com este problema um poderoso e flexível instrumento para modelar a estrutura de dependência entre variáveis aleatórias e que é preferível ao instrumento tradicional baseado na correlação linear. Neste estudo, nós analisamos a dinâmica temporal da estrutura de dependência entre índices de mercados financeiros internacionais e propomos um novo procedimento para capturar a estrutura de dependência ao longo do tempo. Adicionalmente, estudamos alguns fatos estilizados sobre índices de mercados financeiros como a relação entre volume-volatilidade e retorno-volatilidade. / Modelling dependence is of key importance to all economic fields in which uncertainty plays a large role. It is a crucial element of risk analysis and decision making under uncertainty. Copulas offer economic agents facing uncertainty a powerful and flexible tool to model dependence between random variables and often are preferable to the traditional, correlation-based approach. In this work we analyze the time dynamics of the dependence structure between broad stock market indices and propose a novel procedure to capture dependence structure over time. Additionally, we study some stylized facts about stock market indexes such as volume-volatility and return-volatility relations.

A modelagem da estrutura de dependência é de grande importância em todos os ramos da economia onde há incerteza. Ela é um elemento crucial na análise de risco e para a tomada de decisão sob incerteza. As cópulas oferecem aos agentes que se deparam com este problema um poderoso e flexível instrumento para modelar a estrutura de dependência entre variáveis aleatórias e que é preferível ao instrumento tradicional baseado na correlação linear. Neste estudo, nós analisamos a dinâmica temporal da estrutura de dependência entre índices de mercados financeiros internacionais e propomos um novo procedimento para capturar a estrutura de dependência ao longo do tempo. Adicionalmente, estudamos alguns fatos estilizados sobre índices de mercados financeiros como a relação entre volume-volatilidade e retorno-volatilidade. / Modelling dependence is of key importance to all economic fields in which uncertainty plays a large role. It is a crucial element of risk analysis and decision making under uncertainty. Copulas offer economic agents facing uncertainty a powerful and flexible tool to model dependence between random variables and often are preferable to the traditional, correlation-based approach. In this work we analyze the time dynamics of the dependence structure between broad stock market indices and propose a novel procedure to capture dependence structure over time. Additionally, we study some stylized facts about stock market indexes such as volume-volatility and return-volatility relations.

A modelagem da estrutura de dependência é de grande importância em todos os ramos da economia onde há incerteza. Ela é um elemento crucial na análise de risco e para a tomada de decisão sob incerteza. As cópulas oferecem aos agentes que se deparam com este problema um poderoso e flexível instrumento para modelar a estrutura de dependência entre variáveis aleatórias e que é preferível ao instrumento tradicional baseado na correlação linear. Neste estudo, nós analisamos a dinâmica temporal da estrutura de dependência entre índices de mercados financeiros internacionais e propomos um novo procedimento para capturar a estrutura de dependência ao longo do tempo. Adicionalmente, estudamos alguns fatos estilizados sobre índices de mercados financeiros como a relação entre volume-volatilidade e retorno-volatilidade. / Modelling dependence is of key importance to all economic fields in which uncertainty plays a large role. It is a crucial element of risk analysis and decision making under uncertainty. Copulas offer economic agents facing uncertainty a powerful and flexible tool to model dependence between random variables and often are preferable to the traditional, correlation-based approach. In this work we analyze the time dynamics of the dependence structure between broad stock market indices and propose a novel procedure to capture dependence structure over time. Additionally, we study some stylized facts about stock market indexes such as volume-volatility and return-volatility relations.

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.

There has been an on-going debate about choices of the most suitable model amongst a variety of model specifications and parameterizations. The first dissertation essay investigates whether asymmetric leptokurtic return distributions such as Hansen's (1994) skewed tdistribution combined with GARCH specifications can outperform mixed GARCH-jump models such as Maheu and McCurdy's (2004) GARJI model incorporating the autoregressive conditional jump intensity parameterization in the discrete-time framework. I find that the more parsimonious GJR-HT model is superior to mixed GARCH-jump models. Likelihood-ratio (LR) tests, information criteria such as AIC, SC, and HQ and Value-at-Risk (VaR) analysis confirm that GJR-HT is one of the most suitable model specifications which gives us both better fit to the data and parsimony of parameterization. The benefits of estimating GARCH models using asymmetric leptokurtic distributions are more substantial for highly volatile series such as emerging stock markets, which have a higher degree of non-normality. Furthermore, Hansen's skewed t-distribution also provides us with an excellent risk management tool evidenced by VaR analysis. The second dissertation essay provides a variety of empirical evidences to support redundancy of stochastic volatility for SP500 index returns when stochastic volatility is taken into account with infinite activity pure Lévy jumps models and the importance of stochastic volatility to reduce pricing errors for SP500 index options without regard to jumps specifications. This finding is important because recent studies have shown that stochastic volatility in a continuous-time framework provides an excellent fit for financial asset returns when combined with finite-activity Merton's type compound Poisson jump-diffusion models. The second essay also shows that stochastic volatility with jumps (SVJ) and extended variance-gamma with stochastic volatility (EVGSV) models perform almost equally well for option pricing, which strongly imply that the type of Lévy jumps specifications is not important factors to enhance model performances once stochastic volatility is incorporated. In the second essay, I compute option prices via improved Fast Fourier Transform (FFT) algorithm using characteristic functions to match arbitrary log-strike grids with equal intervals with each moneyness and maturity of actual market option prices.

Submitted by RENATO MORI (rmori3@hotmail.com) on 2017-09-20T05:58:01Z No. of bitstreams: 1 dissertacao_VaRArmaGarchSkewt.pdf: 3267680 bytes, checksum: 6a8a935c128bb04a8a4f91fb592de3a8 (MD5) / Approved for entry into archive by Thais Oliveira (thais.oliveira@fgv.br) on 2017-09-20T17:58:58Z (GMT) No. of bitstreams: 1 dissertacao_VaRArmaGarchSkewt.pdf: 3267680 bytes, checksum: 6a8a935c128bb04a8a4f91fb592de3a8 (MD5) / Made available in DSpace on 2017-09-21T13:36:32Z (GMT). No. of bitstreams: 1 dissertacao_VaRArmaGarchSkewt.pdf: 3267680 bytes, checksum: 6a8a935c128bb04a8a4f91fb592de3a8 (MD5) Previous issue date: 2017-08-22 / A proposta do estudo é aplicar ao Ibovespa, modelo paramétrico de VaR de 1 dia, com distribuição dos retornos dinâmica, que procura apreciar características empíricas comumente apresentadas por séries financeiras, como clusters de volatilidade e leptocurtose. O processo de retornos é modelado como um ARMA com erros GARCH que seguem distribuição t assimétrica. A metodologia foi comparada com o RiskMetrics e com modelos ARMA-GARCH com distribuição dos erros normal e t. Os modelos foram estimados diariamente usando uma janela móvel de 1008 dias. Foi verificado pelos backtests de Christoffersen e de Diebold, Gunther e Tay que dentre os modelos testados, o ARMA(2,2)- GARCH(2,1) com distribuição t assimétrica apresentou os melhores resultados. / The proposal of the study is to apply to Ibovespa a 1 day VaR parametric model, with dynamic distribution of returns, that aims to address empirical features usually seen in financial series, such as volatility clustering and leptocurtosis. The returns process is modeled as an ARMA with GARCH residuals that follow a skewed t distribution. The methodology was compared to RiskMetrics and to ARMA-GARCH with normal and t distributed residuals. The models were estimated every daily period using a window of 1008 days. By the backtests of Christoffersen and Diebold, Gunther and Tay, among the tested models, the ARMA(2,2)-GARCH(2,1) with skewed t distribution has given the best results.