In this study, different from previous studies, the explanatory power of Student-t distribution is compared to normal distribution by employing both standard GARCH and EGARCH models to dollar/ lira (USD/TRY) exchange rate. Then the impact of Central Bank of Republic of the Turkey&rsquo / s (CBRT) decisions and actions on both the level of exchange rate and the volatility is investigated. Moreover the relationship between volatility and market liquidity is examined using spot foreign exchange (FX) market volume as a proxy. The results reveal that, in contrast to preceding findings, Student-t could not capture the leptokurtic property better than normal distribution does. Furthermore, an increase in Turkish government benchmark bond rates, CBRT FX purchase interventions and announcement of suspending/ decreasing-the-amount-of FX auctions lead Turkish lira to depreciate. Because of the significant positive leverage effect, the results of GARCH and EGARCH variance equations differ so much. Thereby the results should be evaluated cautiously. In addition it is observed that, only EGARCH model gives significant results when the spot market trading volume is included in the models

Os programas de Ensaios de Prociência (EP) são utilizados pela sociedade para avaliar a competência e a confiabilidade de laboratórios na execução de medições específicas. Atualmente, diversos grupos de EP foram estabelecidos pelo INMETRO, entre estes, o grupo de testes de motores. Cada grupo é formado por diversos laboratórios que medem o mesmo artefato e suas medições são comparadas através de métodos estatísticos. O grupo de motores escolheu um motor gasolina 1.0, gentilmente cedido pela GM Powertrain, como artefato. A potência do artefato foi medida em 10 pontos de rotação por 6 laboratórios. Aqui, motivados por este conjunto de dados, estendemos o modelo de calibração comparativa de Barnett (1969) para avaliar a compatibilidade dos laboratórios considerando a distribuição t de Student e apresentamos os resultados obtidos das aplicações e simulações a este conjunto de dados / Proficiency Testing (PT) programs are used by society to assess the competence and the reliability in laboratories execution of specific measurements. Nowadays many PT groups were established by INMETRO, including the motor\'s test group. Each group is formed by laboratories measuring the same artifact and their measurements are compared through statistic methods. The motor\'s group chose a gasoline engine 1.0, kindly provided by GM as an artifact. The artifact\'s power was measured at ten points of rotation by 6 laboratories. Here, motivated by this set data, we extend the Barnet comparative calibration model (1969) to assess the compatibility of the laboratories considering the Student-t distribution and show the results obtained from application and simulation of this set data

We define and study multivariate and matrix variate skew Pearson type VII and skew t-distributions. We derive the marginal and conditional distributions, the linear transformation, and the stochastic representations of the multivariate and matrix variate skew Pearson type VII distributions and skew t-distributions. Also, we study the limiting distributions.

An effective risk management program requires reliable risk measurement. Failure to assess inherited risks in mortgage-backed securities in the U.S. market contributed to the financial crisis of 2007–2008, which has prompted government regulators to pay greater attention to controlling risk in banks, investment funds, credit unions, and other financial institutions to prevent bankruptcy and financial crisis in the future. In order to calculate risk in a reliable manner, this thesis has focused on the statistical modeling of expected return and volatility. The primary aim of this study is to propose a framework, based on the probabilistic reduction approach, to reliably quantify market risk using statistical models and historical data. Particular emphasis is placed on the importance of the validity of the probabilistic assumptions in risk measurement by demonstrating how a statistically misspecified model will lead the evaluation of risk astray. The concept of market risk is explained by discussing the narrow definition of risk in a financial context and its evaluation and implications for financial management. After highlighting empirical evidence and discussing the limitations of the ARCH-GARCH-type volatility models using exchange rate and stock market data, we proposed Student's t Autoregressive models to estimate expected return and volatility to measure risk, using Value at Risk (VaR) and Expected Shortfall (ES). The misspecification testing analysis shows that our proposed models can adequately capture the chance regularities in exchange rates and stock indexes data and give a reliable estimation of regression and skedastic functions used in risk measurement. According to empirical findings, the COVID-19 pandemic in the first quarter of 2020 posed an enormous risk to global financial markets. The risk in financial markets returned to levels prior to the COVID-19 pandemic in 2021, after COVID-19 vaccine distribution started in developed countries. / Doctor of Philosophy / Reliable risk measurement is necessary for any effective risk management program. Hence, the primary purpose of this dissertation was to propose a framework to quantify market risk using statistical models and historical data, with a particular emphasis placed on checking the validity of probabilistic assumptions underlying models. After discussing the concept of market risk and its evaluation methods in financial management, we explored the empirical evidence in financial data and highlighted some limitations of other well-known modeling approaches. In order to ameliorate limitations, this study proposed Student's t Autoregressive models to estimate the conditional mean and the conditional variance of the financial variables and use them to measure risk via two popular methods: Value at Risk (VaR) and Expected Shortfall (ES). Further investigation shows that our proposed models can adequately model exchange rates and stock indexes data and give reliable estimations to use in risk measurement. We used our model to quantify risk in global financial markets in recent years. The results show that the COVID-19 pandemic posed an enormous risk to global financial markets in the first quarter of 2020. In 2021, the level of risk in financial markets returned to levels before the COVID-19 pandemic, after COVID-19 vaccine distribution started in developed countries.

Following the Probabilistic Reduction(PR) Approach, this paper proposes the Student’s Autoregressive (St-AR) Model, Student’s t Vector Autoregressive (St-VAR) Model and their heterogeneous versions, as an alternative to the various ARCH type models, to capture univariate and multivariate volatility. The St-AR and St-VAR models differ from the latter volatility models because they give rise to internally consistent statistical models that do not rely on ad-hoc specification and parameter restrictions, but model the conditional mean and conditional variance jointly. The univariate modeling is illustrated using the Real Effect Exchange Rate(REER) indices of three mainstream currencies in Asia (RMB, Hong Kong Dollar and Taiwan Dollar), while the multivariate volatility modeling is applied to investigate the relationship between the REER indices and stock price indices in mainland China, as well as the relationship between the stock prices in mainland China and Hong Kong. Following the PR methodology, the information gained in Mis-Specification(M-S) testing leads to respecification strategies from the original Normal-(V)AR models to the St-(V)AR models. The results from formal Mis-Specification (M-S) tests and forecasting performance indicate that the St-(V)AR models provide a more appropriate way to model volatility for certain types of speculative price data. / Ph. D.

此論文研究有什麼因子會影響台灣股票加權指數報酬率之偏態係數。過去的文獻顯示，交易量和報酬率為可能的因子。實證的結果確實發現，交易量和報酬率顯著地影響偏態係數。 / This study examines the determinants for conditional skewness of the return distribution of the Taiwan Stock Exchange Value-Weighted Index. Important driving factors that affect conditional skewness, based on the theory literature, include trading volumes and returns. To capture the skewness in the data, the family of time series model we consider focuses on the specifications of higher-order moments than mean and volatility that conventional models look at. With the specifications, we are able to test whether the factors, volumes and returns, can influence conditional skewnees of the return distribution. Our results suggest the significance of the factors using data from the Taiwan Stock Exchange Value-Weighted Index.

We define and study multivariate and matrix variate skew Pearson type VII and skew t-distributions. We derive the marginal and conditional distributions, the linear transformation, and the stochastic representations of the multivariate and matrix variate skew Pearson type VII distributions and skew t-distributions. Also, we study the limiting distributions.

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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.

In this dissertation, we approach three different contributions in measurement error model (MEM). Initially, we carry out maximum penalized likelihood inference in MEMs under the normality assumption. The methodology is based on the method proposed by Firth (1993), which can be used to improve some asymptotic properties of the maximum likelihood estimators. In the second contribution, we develop two new estimation methods based on generalized fiducial inference for the precision parameters and the variability product under the Grubbs model considering the two-instrument case. One method is based on a fiducial generalized pivotal quantity and the other one is built on the method of the generalized fiducial distribution. Comparisons with two existing approaches are reported. Finally, we propose to study inference in a heteroscedastic MEM with known error variances. Instead of the normal distribution for the random components, we develop a model that assumes a skew-t distribution for the true covariate and a centered Students t distribution for the error terms. The proposed model enables to accommodate skewness and heavy-tailedness in the data, while the degrees of freedom of the distributions can be different. We use the maximum likelihood method to estimate the model parameters and compute them via an EM-type algorithm. All proposed methodologies are assessed numerically through simulation studies and illustrated with real datasets extracted from the literature. / Neste trabalho abordamos três contribuições diferentes em modelos com erros de medição (MEM). Inicialmente estudamos inferência pelo método de máxima verossimilhança penalizada em MEM sob a suposição de normalidade. A metodologia baseia-se no método proposto por Firth (1993), o qual pode ser usado para melhorar algumas propriedades assintóticas de os estimadores de máxima verossimilhança. Em seguida, propomos construir dois novos métodos de estimação baseados na inferência fiducial generalizada para os parâmetros de precisão e a variabilidade produto no modelo de Grubbs para o caso de dois instrumentos. O primeiro método é baseado em uma quantidade pivotal generalizada fiducial e o outro é baseado no método da distribuição fiducial generalizada. Comparações com duas abordagens existentes são reportadas. Finalmente, propomos estudar inferência em um MEM heterocedástico em que as variâncias dos erros são consideradas conhecidas. Nós desenvolvemos um modelo que assume uma distribuição t-assimétrica para a covariável verdadeira e uma distribuição t de Student centrada para os termos dos erros. O modelo proposto permite acomodar assimetria e cauda pesada nos dados, enquanto os graus de liberdade das distribuições podem ser diferentes. Usamos o método de máxima verossimilhança para estimar os parâmetros do modelo e calculá-los através de um algoritmo tipo EM. Todas as metodologias propostas são avaliadas numericamente em estudos de simulação e são ilustradas com conjuntos de dados reais extraídos da literatura