This thesis focuses on impact of jumps and simultaneous jumps (co-jumps) in asset prices on future volatility. Our main contribution to the empirical literature lies in the use of panel Heterogeneous Autoregressive (HAR) model that allows us to obtain average effect of jumps for both the portfolio of 29 U.S. stocks and 8 individual market sectors our stocks belong to. On top of that we investigate the effect of sign for both jumps and co-jumps. The estimation results indicate that the impact of jumps on future volatility is positive whereas for co-jumps it is negative. We also document tendency of downward jumps and co-jumps to be followed by increase in volatility and that upward jumps and co-jumps are followed by decrease in volatility. Finally, results for individual sectors reveal that estimated effects vary across industries - for cyclical sectors volatility is in general more sensitive to negative jumps and less sensitive to positive jumps than for defensive sectors.

This thesis analyzes the use of realized moments in asset pricing. The analysis is done using dataset containing log-returns for 29 of the most traded stocks and covering 10 years of data. The dataset is split into training set covering 7 years and test set covering 3 years of data. For each of the stocks a separate time series model is estimated. In evaluation of the quality of the models, metrics such as RMSE, MAD, accuracy in forecasting the sign of future returns, and returns achievable by executing trades based on the recommendations from the model are used. Even though the inclusion of realized moments does not provide significant improvements in terms of RMSE, it is found that realized skewness and kurtosis significantly contribute to explaining the returns of individual stocks as they lead to consistent improvements in identifying future positive, as well as negative, returns. Moreover, the recommendations from the models using realized moments can help us achieve significantly higher returns from trading stocks. Inclusion of the interaction terms for variance and returns, skewness and returns, and kurtosis and variance, provides additional improvement of forecasting accuracy, as well as improvements in returns achievable by executing transactions based on recommendations from the 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.

O estudo da volatilidade dos retornos dos ativos ocupa um lugar de destaque dentro da moderna teoria de finanças. Tradicionalmente, os modelos empregados para a modelagem da volatilidade são estimados a partir de dados diários. No entanto, a recente disponibilidade de dados intradiários tem permitido a modelagem e a previsão da volatilidade dos ativos por meio da chamada variância realizada. Dessa forma, o objetivo principal da presente dissertação foi analisar como os modelos que incorporam dados intradiários se comportam, em termos de acurácia de previsão de volatilidade diária, em relação àqueles que utilizam apenas dados diários. Foram observados os comportamentos dos índices Ibovespa e S&P 500 durante o período de janeiro de 2006 a junho de 2009. Os resultados revelaram que o desempenho de previsão dos modelos estimados a partir de dados diários foi superior ao dos modelos de variância realizada para os dois índices. Buscou-se ainda comparar o comportamento dos modelos durante o período da crise de 2008. Novamente os resultados apontaram para uma melhor acurácia de previsão dos modelos que utilizaram apenas dados diários. / The study of volatility in asset returns is relevant within the modern theory of finance. Modeling volatility has been frequently based on daily data. Recent availability of intraday data has allowed volatility modeling and forecasting through the so called realized variance. The main objective of this master’s thesis was, therefore, to compare the accuracy of daily volatility forecasting between models that use either daily or intraday data. Returns during the period January 2006 to June 2009 on two indexes, the Ibovespa and the S&P 500, were used. Results showed that, for both indexes, forecasting based on daily data was superior to forecasting that used intraday returns. Comparison between models was also tested during the 2008 crisis. Similarly, results showed a better forecasting performance of daily data models.

The thesis is focused on the issue of Apartment price heat maps. The aim is to approach the topic of apartment price heat maps, methodology for the creation of price heat maps and its specifics. Theoretical knowledge is applied to two selected parts of Prague - Zizkov and Vinohrady. The final data of both areas are summarised to two specific price heat maps. The end of the thesis compares the processed results with officially published data of the czech national institution ČSÚ.

Many past literatures have examined the predictive power of implied volatility versus that of historical volatility, but they have showed divergent conclusions. One of the major differences among these studies is the methods that they used to obtain implied volatility. The VIX index, introduced in 1993, provides a model-free and directly observable source of implied volatility data. The VIX futures is an actively traded VIX derivative product, and its prices are believed to contain market’s expectation about future volatility. By analyzing the relationship between the VIX futures prices and the realized volatilities of the 30-day period that these VIX futures contracts cover, this paper finds that the VIX futures contracts with shorter maturities have predictive power on future realized volatility, but they are upwardly biased estimates. The predictive power, however, decreases as the time to maturity increases. The outstanding VIX futures contracts with the nearest expiration dates outperform GARCH estimates based on historical return data at predicting future realized volatility.

Estimating the integrated volatility of high frequency realized prices is an important issue in microstructure literature. Bandi and Russell (2006) derived the optimal-sampling frequency, and Zhang et al. (2005) proposed a "two-scales estimator" to solve the problem. In this study, we propose a new estimator based on a signal to noise ratio statistic with convergence rate of Op (n^(−1/ 4) ). The method is applicable to both constant and stochastic volatility models and modi¡Âes the Op (n^(−1/ 6) ) convergence rate of Zhang et al. (2005). The proposed estimator is shown to be asymptotic e¡Ócient as the maximum likelihood estimate for the constant volatility case. Furthermore, unbiased estimators of the two elements, the variance of the microstructure noise and the fourth moment of the realized log returns, are also proposed to facilitate the estimation of integrated volatility. The asymptotic prop- erties and e®ectiveness of the proposed estimators are investigated both theoretically and via simulation study.

The purpose of this thesis is to evaluate five different volatility forecasting models that are used to calculate financial market risk. The models are used on both daily exchange rates and high-frequency intraday data from four different series. The results show that time series models fitted to high-frequency intraday data together with a critical value taken from the empirical distribution displayed the best forecasts overall.

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