Zugl.: Osnabrück, Univ., Diss., 2005

<p>The paper is devoted to the modern methods of Value-at-Risk calculation using different cases of Generalized Hyperbolic distribution and models for predicting volatility. In our research we use GARCH-M and Non-parametric volatility models and compare Value-at-Risk calculation depending on the distribution that is used. In the case of Non-parametric model corresponding windows are proved by the Cross Validation method. Furthermore in our work we consider adaption of the method to intraday data using ACD and UHF-GARCH models. The project involves also application of the developed methods to real financial data and comparable analysis of the obtained results.</p>

The paper is devoted to the modern methods of Value-at-Risk calculation using different cases of Generalized Hyperbolic distribution and models for predicting volatility. In our research we use GARCH-M and Non-parametric volatility models and compare Value-at-Risk calculation depending on the distribution that is used. In the case of Non-parametric model corresponding windows are proved by the Cross Validation method. Furthermore in our work we consider adaption of the method to intraday data using ACD and UHF-GARCH models. The project involves also application of the developed methods to real financial data and comparable analysis of the obtained results.

Thesis (doctoral)--Universität, Göttingen, 2000.

This thesis consists of three research topics, which together study the related topics of volatility jumps, modeling volatility and forecasting Value-at-­Risk (VaR). The first topic focuses on volatility jumps based on two recently developed jumps detection methods and empirically studied six markets and the distributional features, size and intensity of jumps and cojumps. The results indicate that foreign exchange markets have higher jump intensities, while equity markets have a larger jump size. I find that index and stock markets have more interdependent cojumps across markets. I also find two recently proposed jump detection methods deliver contradictory results of jump and cojump properties. The jump detection technique based on realized outlyingness weighted variation (ROWV) delivers higher jump intensities in foreign exchange markets, whereas the bi-­power variation (BV) method produces higher jump intensities in equity markets. Moreover, jumps under the ROWV method display more serial correlations than the BV method. The ROWV method detects more cojumps and higher cojumps intensities than the BV method does, particularly in foreign exchange markets. In the second topic, the Model Confidence Set test (MCS) is used. MCS selects superior models by power in forecasting ability. The candidate models set included 9 GARCH type models and 8 realized volatility models. The dataset is based on six markets spanning more than 10 years, avoiding the so-called data snooping problem. The dataset is extended by including recent financial crisis periods. The advantage of the MCS test is that it can compare models in a group, not only in a pair. Two loss functions that are robust to noise in volatility proxy were also implemented and the empirical results indicated that the traditional GARCH models were outperformed by realized volatility models when using intraday data. The MCS test based on MSE selected asymmetric ARFIMA models and the HAR mode as the most predictive, while the asymmetric QLike loss function revealed the leveraged HAR and leveraged HAR-­CJ model based on bi-­power variation as the highest performers. Moreover, results from the subsamples indicate that the asymmetric ARFIMA model performs best over turbulent periods. The third topic focuses on evaluating a broad band of VaR forecasts. Different VaR models were compared across six markets, five volatility models, four distributions and 8 quantiles, resulting in 960 specifications. The MCS test based on regulatory favored asymmetric loss function was applied and the empirical results indicate that the proposed asymmetric ARFIMA and leveraged HAR models, coupled with generalized extreme value distribution (GEV) or generalized Pareto distribution (GPD), have the superior predictive ability on both long and short positions. The filtered extreme value methods were found to handle not only extreme quantiles but also regular ones. The analysis conducted in this thesis is intended to aid risk management, and subsequently reduce the probability of financial distress in the sector.

FERREIRA, Antonio Glênio Moura. Gestão de risco das principais tesourarias de fundos de investimento em ações no Brasil. 2014. 74 f. Dissertação (Mestrado Profissional) - Programa de Pós Graduação em Economia, CAEN, Universidade Federal do Ceará, Fortaleza-CE, 2014. / Submitted by Mônica Correia Aquino (monicacorreiaaquino@gmail.com) on 2014-11-26T19:15:33Z No. of bitstreams: 1 2014_dissert_agmferreira.pdf: 4707768 bytes, checksum: f18c9c30d647c9b0285c6569738e1f47 (MD5) / Approved for entry into archive by Mônica Correia Aquino(monicacorreiaaquino@gmail.com) on 2014-11-26T19:15:47Z (GMT) No. of bitstreams: 1 2014_dissert_agmferreira.pdf: 4707768 bytes, checksum: f18c9c30d647c9b0285c6569738e1f47 (MD5) / Made available in DSpace on 2014-11-26T19:15:47Z (GMT). No. of bitstreams: 1 2014_dissert_agmferreira.pdf: 4707768 bytes, checksum: f18c9c30d647c9b0285c6569738e1f47 (MD5) Previous issue date: 2014 / This study aims to examine empirically the behavior of the model for measuring market risk Value at Risk - VaR in its parametric interpretation unconditional Gaussian and extensions that regulate violations on heteroscedasticity and non-normality of daily returns of investment funds Actions, of the thirteen largest financial institutions resident in Brazil, during the January/06 dezembro/12. For a better evaluation of the data, we sought to initially model the conditional evolution of risk and adjust the statistic al idiosyncrasy of temporal series of thirteen treasuries, using probability distributions that best adapt to the analysis of the models. The results obtained with the semodels are analyzed by the test failure rate proposed by Kupiec (1995) and Chisttoffersen (1998). The survey also shows, with graphic examples, a performance Risk - Return of the thirteen banks using the methodology proposed by Balzer. / O presente trabalho busca analisar, empiricamente, o comportamento do modelo de mensuração de risco de mercado Value-at-Risk – VaR em sua interpretação paramétrica gaussiana incondicional e extensões que regulam as violações sobre a não normalidade e a heterocedasticidade dos retornos diários dos fundos de investimentos em Ações, das treze maiores instituições financeiras residentes no Brasil, durante o período de janeiro/06 a dezembro/12. Para uma melhor avaliação dos dados, buscou-se, inicialmente, modelar a evolução condicional do risco e ajustar a idiossincrasia estatística das séries temporais das treze tesourarias, utilizando distribuições de probabilidade que mais se adaptassem à análise dos modelos. Os resultados obtidos com esses modelos são analisados à luz do teste para proporção de falhas proposto por Kupiec (1995) e Chisttoffersen (1998). A pesquisa ainda apresenta, com exemplos gráficos, uma análise de desempenho Risco – Retorno dos treze bancos utilizando a metodologia proposta por Balzer.

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.

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.

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.

The focus of my research has been computationally efficient means of computing measures of risk for portfolios of nonlinear financial instruments when the risk factors might be possibly non-Gaussian. In particular, the measures of risk chosen have been Value-at-Risk (VaR) and conditional Value-at-Risk (CVaR). I have studied the problem of computation of risk in two types of financial portfolios with nonlinear instruments which depend on possibly non-Gaussian risk factors: 1. Portfolios of European stock options when the stock return distribution may not be Gaussian; 2. Portfolios of sovereign bonds (which are nonlinear in the underlying risk factor, i.e. the short rate) when the risk factor may or may not be Gaussian. Addressing both these problems need a wide array of mathematical tools both from the field of applied statistics (Delta-Gamma-Normal models, characteristic function inversion, probability conserving transformation) and systems theory (Vasicek stochastic differential equation model, Kalman filter). A new heuristic is proposed for addressing the first problem, while an empirical study is presented to support the use of filter-based models for addressing the second problem. In addition to presenting a discussion of these underlying mathematical tools, the dissertation also presents comprehensive numerical experiments in both cases, with simulated as well as real financial market data. Backtesting is used to confirm the validity of the proposed methods.