The focus of this thesis is on the employment of theoretical and practical quantile methods in addressing prediction, risk measurement and inference problems. From a prediction perspective, a problem of creating model-free prediction intervals for a future unobserved value of a random variable drawn from a sample distribution is considered. With the objective of reducing prediction coverage error, two common distribution transformation methods based on the normal and exponential distributions are presented and they are theoretically demonstrated to attain exact and error-free prediction intervals respectively. The second problem studied is that of estimation of expected shortfall via kernel smoothing. The goal here is to introduce methods that will reduce the estimation bias of expected shortfall. To this end, several one-step bias correction expected shortfall estimators are presented and investigated via simulation studies and compared with one-step estimators. The third problem is that of constructing simultaneous confidence bands for quantile regression functions when the predictor variables are constrained within a region is considered. In this context, a method is introduced that makes use of the asymmetric Laplace errors in conjunction with a simulation based algorithm to create confidence bands for quantile and interquantile regression functions. Furthermore, the simulation approach is extended to an ordinary least square framework to build simultaneous bands for quantiles functions of the classical regression model when the model errors are normally distributed and when this assumption is not fulfilled. Finally, attention is directed towards the construction of prediction intervals for realised volatility exploiting an alternative volatility estimator based on the difference of two extreme quantiles. The proposed approach makes use of AR-GARCH procedure in order to model time series of intraday quantiles and forecast intraday returns predictive distribution. Moreover, two simple adaptations of an existing model are also presented.

[pt] A expansão do mercado de derivativos no mundo e principalmente no Brasil tem impulsionado seus usuários a aprimorar e desenvolver ferramentas de apreçamento mais eficientes. Com esse intuito, o presente trabalho tem por objetivo evidenciar qual janela de observações gera a curtose e a assimetria que mais suavize o sorriso da volatilidade utilizando-se do modelo Corrado-Su. Para tanto, as empresas escolhidas foram a Petrobrás PN e a Vale PNA, devido a suas ações e opções de compra serem as mais líquidas no mercado brasileiro. A análise dos dados apontou para uma maior suavização do sorriso da volatilidade por parte das janelas de dados de curto prazo sobre as longo prazo, e uma equivalência de desempenho das primeiras ao do modelo Black-Scholes. / [en] The expansion of the derivatives market in the world and especially in Brazil has driven its users to enhance and develop tools for more efficient pricing. With this purpose, this paper aims to point which window of observations generates the kurtosis and skewness that more soften the volatility smile using the Corrado-Su model. Therefore, the firms that were chosen were Petrobras PN and Vale PNA, because their stocks and options are the most liquid in Brazilian market. The data analysis indicated a greater smoothing volatility smile using the windows of observations of the short term instead of the long term, and a equivalent performance of the first ones to that of the Black-Scholes model.

[pt] Algumas literaturas sugerem que a volatilidade implícita das opções de compra de ações não deve ser utilizada como estimador para a volatilidade futura. Contudo, estudos recentes e aplicados ao mercado brasileiro de ações comprovaram que em determinados casos existe relação entre a volatilidade implícita e a volatilidade real (ou realizada). Isso significa dizer que a primeira traz informações sobre a última. Nesse contexto, o objetivo deste estudo é comparar a volatilidade implícita de dois modelos de apreçamento de opções com a volatilidade realizada. Entre os modelos de Black-Scholes (1973) e Corrado-Su (1996), utilizando dados de opções de Petrobras e Vale do Rio Doce, foram calculados, através do erro quadrático, aqueles resultados que mais se aproximaram da volatilidade realizada. Estes resultados trazem indícios de que o modelo de Black-Scholes, em média, foi superior ao Corrado-Su no período que vai de janeiro de 2005 a julho de 2009. Porém, o último, por levar em consideração a assimetria e a curtose da distribuição de retornos, chegou mais perto da volatilidade realizada apenas em alguns momentos específicos das economias brasileira e mundial. / [en] Several authors have proposed that implied volatility from purchase options should not be used as an estimate for future volatility. However, recent studies applied to the Brazilian stock market proved that in certain cases there is relation between implied volatility and realized volatility. This means that the first one provides information on the last. In this context, the objective of this study is to compare implied volatilities from two different option pricing models against the realized volatility. The models are Black-Scholes (1973) and Corrado-Su (1996). Working with purchase options on Petrobras and Vale do Rio Doce, it was calculated the difference, by quadratic error, between the implied volatility of these models and the realized volatility. After this, it was checked those results that came closer to the realized volatility. The results provide evidence that the Black-Scholes model, on average, has higher performance than Corrado-Su from January 2005 to July 2009. However, Corrado-Su by taking into account the asymmetry and kurtosis of the distribution of returns came closer to the realized volatility only in specific moments of the Brazilian and global economies.

Neste trabalho realizamos um amplo estudo de simulação com o objetivo principal de avaliar o desempenho de carteiras de mínima variância global construídas com base em modelos de previsão da volatilidade que utilizam dados de alta frequência (em comparação a dados diários). O estudo é baseado em um abrangente conjunto de dados financeiros, compreendendo 41 ações listadas na BM&FBOVESPA entre 2009 e 2017. Nós avaliamos modelos de previsão de volatilidade que são inspirados na literatura ARCH, mas que também incluem medidas realizadas. Eles são os modelos GARCH-X, HEAVY e Realized GARCH. Seu desempenho é comparado com o de carteiras construídas com base na matriz de covariância amostral, métodos de encolhimento e DCC-GARCH, bem como com a carteira igualmente ponderada e o índice Ibovespa. Uma vez que a natureza do trabalho é multivariada, e a fim de possibilitar a estimação de matrizes de covariância de grandes dimensões, recorremos à especificação DCC. Utilizamos três frequências de rebalanceamento (diária, semanal e mensal) e quatro conjuntos diferentes de restrições sobre os pesos das carteiras. A avaliação de desempenho baseia-se em medidas econômicas tais como retornos anualizados, volatilidade anualizada, razão de Sharpe, máximo drawdown, Valor em Risco, Valor em Risco condicional e turnover. Como conclusão, para o nosso conjunto de dados o uso de retornos intradiários (amostrados a cada 5 e 10 minutos) não melhora o desempenho das carteiras de mínima variância global. / In this work we perform an extensive backtesting study targeting as a main goal to assess the performance of global minimum variance (GMV) portfolios built on volatility forecasting models that make use of high frequency (compared to daily) data. The study is based on a broad intradaily financial dataset comprising 41 assets listed on the BM&FBOVESPA from 2009 to 2017. We evaluate volatility forecasting models that are inspired by the ARCH literature, but also include realized measures. They are the GARCH-X, the High-Frequency Based Volatility (HEAVY) and the Realized GARCH models. Their perfomances are benchmarked against portfolios built on the sample covariance matrix, covariance matrix shrinkage methods, DCC-GARCH as well as the naive (equally weighted) portfolio and the Ibovespa index. Since the nature of this work is multivariate and in order to make possible the estimation of large covariance matrices, we resort to the Dynamic Conditional Correlation (DCC) specification. We use three different rebalancing schemes (daily, weekly and monthly) and four different sets of constraints on portfolio weights. The performance assessment relies on economic measures such as annualized portfolio returns, annualized volatility, Sharpe ratio, maximum drawdown, Value at Risk, Expected Shortfall and turnover. We also account for transaction costs. As a conclusion, for our dataset the use of intradaily returns (sampled every 5 and 10 minutes) does not enhance the performance of GMV portfolios.

Volatility spillovers in stock markets have become an important phenomenon, especially in times of crises. Mechanisms of shock transmission from one mar- ket to another are important for the international portfolio diversification. Our thesis examines impulse responses and variance decomposition of main stock in- dices in emerging Central European markets (Czech Republic, Poland, Slovakia and Hungary) in the period of January 2007 to August 2009. Two models are used: A vector autoregression (VAR) model with constant variance of resid- uals and a time varying parameter vector autoregression (TVP-VAR) model with a stochastic volatility. Opposingly of other comparable studies, Bayesian methods are used in both models. Our results confirm the presence of volatility spillovers among all markets. Interestingly, we find significant opposite trans- mission of shocks from Czech Republic to Poland and Hungary, suggesting that investors see the Central European exchanges as separate markets. Bibliographic Record Janhuba, R. (2012): Volatility Spillovers in New Member States: A Bayesian Model. Master thesis, Charles University in Prague, Faculty of Social Sciences, Institute of Economic Studies. Supervisor: doc. Roman Horváth Ph.D. JEL Classification C11, C32, C58, G01, G11, G14 Keywords Volatility spillovers,...

Since the founding of the People’s Republic of China in 1949, China has experienced ten business cyclical fluctuations. The economic growth was characterized by erratic ups and downs which lasted for several decades. With the economic reform and opening up to the outside world in 1978 as part of Deng Xiaoping’s market-oriented policy, the Chinese economy grew exponentially and the volatility of the GDP growth rate declined significantly. The macroeconomic control policies in the 1980s prevented large fluctuations in the country’s economic development, and smoothed the output volatility further. This study examines the output volatility in China and our result reveals the standard deviation of quarterly output growth rate has declined dramatically. Using the CUSUM squares test and the Quandt-Andrews breakpoint test to identify unknown structure breaks, we identified two structural breaks: 1994:1 towards destabilization and 1998:1 towards stabilization. We then examine the stochastic process for GDP and the result shows that the decrease in volatility can be traced primarily to a decrease in the standard deviation of output shocks. Following this, we reached two other conclusions. First, there is a strong relationship between movements in output volatility and the movements in inflation volatility. Both output and inflation volatilities increased significantly during the third and fourth quarter of 1994 and both dropped sharply after 1996, which followed a similar path over the period. Second, using the standard decomposition of GDP, the decrease in output volatility can be traced to a decrease in the volatility of consumption, investment, and net export, especially rural consumption expenditure and residential investment.

In this paper we use model-free estimates of daily exchange rate volatilities employing high-frequency intraday data, known as Realized Volatility, which is then forecasted with ARMA-models and used to produce one-day-ahead Value-at-Risk predictions. The forecasting accuracy of the method is contrasted against the more widely used ARCH-models based on daily squared returns. Our results indicate that the ARCH-models tend to underestimate the Value-at-Risk in foreign exchange markets compared to models using Realized Volatility

Τις τελευταίες δεκαετίες η υψηλή μεταβλητότητα που παρατηρείται στις χρηματοοικονομικές μεταβλητές, έχει δημιουργήσει έντονη την ανάγκη για αποτελεσματική διαχείριση του κινδύνου. Τα παράγωγα χρηματοοικονομικά προϊόντα παρέχουν τα μέσα για αντιστάθμιση του κινδύνου. Προς αυτή την κατεύθυνση έχει κατασκευασθεί ένας δείκτης που αντιπροσωπεύει την τεκμαρτή μεταβλητότητα των παραγώγων χρηματοοικονομικών προϊόντων, ο δείκτης VIX. Σκοπός της εργασίας είναι η διερεύνηση της σχέσης του δείκτη VIX με την αγορά του S&P500 και η σχέση συνολοκλήρωσης τεκμαρτής και δεσμευμένης μεταβλητότητας του S&P500. / --

A volatilidade implícita é um importante tema no campo das Finanças. Do ponto de vista acadêmico, é crescente o número de pesquisas sobre o conteúdo informacional embutido no preço dos ativos. Na visão do mercado, a volatilidade implícita pode ser negociada diretamente no mercado de derivativos como um ativo, permitindo o seu emprego para diversificação de riscos em carteiras de investimentos. No entanto, o mercado brasileiro carece de um índice de volatilidade oficial e os estudos sobre o tema no Brasil são bastante limitados, sendo urgente a proposta de métodos de obtenção deste índice coerentes com o cenário de liquidez. Assim, essa pesquisa tem como objetivo analisar o conteúdo informacional da volatilidade implícita no Brasil. Para isso foi necessário estimar um índice de volatilidade implícita para o mercado brasileiro (“VIX Brasil”), investigar o impacto da liquidez na volatilidade implícita, analisar a capacidade preditiva da volatilidade implícita em relação à volatilidade realizada futura e verificar a sua eficiência na emissão de sinais de proximidade de eventos de stress. Foram utilizados dados diários sobre o mercado de opções sobre índice de 2002 a 2013. Os principais resultados sugerem que a liquidez das opções afeta a variabilidade da volatilidade implícita ao longo do tempo. Em relação ao conteúdo informacional da volatilidade implícita no Brasil, obteve-se indícios de que (i) há significativa relação com o retorno da bolsa, sendo esta uma relação assimétrica e concentrada nos extremos da distribuição; (ii) a volatilidade implícita brasileira possui informações sobre volatilidade futura realizada além daquela contida na volatilidade histórica, porém é um estimador viesado e ineficiente; (iii) o “VIX Brasil” possui capacidade sinalizadora da proximidade de eventos de stress, em especial quando utiliza-se o limiar de 10% sobre a sua média móvel de 90 dias como abordagem de emissão de sinal. / The Implied volatility is an important topic of research in Finance. From the academics point of view, there is a growing interest in the information embedded in asset prices. From the practitioners view, the implied volatility can be directly traded in the derivatives market as an asset, being a tool for risk diversification in investment portfolios. However, the Brazilian capital market lacks an official volatility index and studies on the subject in Brazil are very limited. Hence, models for volatilities indexes consistent with the liquidity scenario of the Brazilian market are an urgent issue. Thus, this research aims to analyse the information content of implied volatility in Brazil. For achieving this goal, it was necessary to estimate an implied volatility index for the Brazilian market ("VIX Brazil"), to investigate the impact of liquidity in implied volatility, to analyse the predictive power of implied volatility for the future realized volatility and to check its efficiency for issuing early warning signals (EWS) of stress events. Daily data on the options market index over 2002 to 2013 were used. The main results suggest that the liquidity of options affects the variability of implied volatility over time. Regarding the information content of implied volatility in Brazil, evidence was obtained that (i) there is significant relationship with the market return, which is an asymmetric relationship and concentrated at the tails of the probability distribution; (ii) the Brazilian implied volatility has information about the future realized volatility than that contained in the historical volatility, but it´s a biased and inefficient estimator; (iii) the "VIX Brazil" has signalling power concerning the proximity of stress events, especially when it is used the 10% threshold on its moving average 90 days as signal emission approach.

Neste trabalho realizamos um amplo estudo de simulação com o objetivo principal de avaliar o desempenho de carteiras de mínima variância global construídas com base em modelos de previsão da volatilidade que utilizam dados de alta frequência (em comparação a dados diários). O estudo é baseado em um abrangente conjunto de dados financeiros, compreendendo 41 ações listadas na BM&FBOVESPA entre 2009 e 2017. Nós avaliamos modelos de previsão de volatilidade que são inspirados na literatura ARCH, mas que também incluem medidas realizadas. Eles são os modelos GARCH-X, HEAVY e Realized GARCH. Seu desempenho é comparado com o de carteiras construídas com base na matriz de covariância amostral, métodos de encolhimento e DCC-GARCH, bem como com a carteira igualmente ponderada e o índice Ibovespa. Uma vez que a natureza do trabalho é multivariada, e a fim de possibilitar a estimação de matrizes de covariância de grandes dimensões, recorremos à especificação DCC. Utilizamos três frequências de rebalanceamento (diária, semanal e mensal) e quatro conjuntos diferentes de restrições sobre os pesos das carteiras. A avaliação de desempenho baseia-se em medidas econômicas tais como retornos anualizados, volatilidade anualizada, razão de Sharpe, máximo drawdown, Valor em Risco, Valor em Risco condicional e turnover. Como conclusão, para o nosso conjunto de dados o uso de retornos intradiários (amostrados a cada 5 e 10 minutos) não melhora o desempenho das carteiras de mínima variância global. / In this work we perform an extensive backtesting study targeting as a main goal to assess the performance of global minimum variance (GMV) portfolios built on volatility forecasting models that make use of high frequency (compared to daily) data. The study is based on a broad intradaily financial dataset comprising 41 assets listed on the BM&FBOVESPA from 2009 to 2017. We evaluate volatility forecasting models that are inspired by the ARCH literature, but also include realized measures. They are the GARCH-X, the High-Frequency Based Volatility (HEAVY) and the Realized GARCH models. Their perfomances are benchmarked against portfolios built on the sample covariance matrix, covariance matrix shrinkage methods, DCC-GARCH as well as the naive (equally weighted) portfolio and the Ibovespa index. Since the nature of this work is multivariate and in order to make possible the estimation of large covariance matrices, we resort to the Dynamic Conditional Correlation (DCC) specification. We use three different rebalancing schemes (daily, weekly and monthly) and four different sets of constraints on portfolio weights. The performance assessment relies on economic measures such as annualized portfolio returns, annualized volatility, Sharpe ratio, maximum drawdown, Value at Risk, Expected Shortfall and turnover. We also account for transaction costs. As a conclusion, for our dataset the use of intradaily returns (sampled every 5 and 10 minutes) does not enhance the performance of GMV portfolios.