This study tests if historical volatility- and implied volatility has significant predictive power over future realized volatility and if so which one of the two is the superior predictor. The study is conducted by using historical volatility of the OMXS30 and implied volatility from OMXS30 call options during the period 2012-2023. Three regressions have been made to test the research questions, two simple linear regression and one multiple linear regression. The results of the study showed that both historical- and implied volatility had significant predictive power over future realized volatility with implied being the superior one with a higher correlation coefficient. The multiple regression showed that both the independent variables were important and both of them explained different parts of the data, which means that they have complementary abilities and that both should be used when assessing the forecast of realized volatility.

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The present thesis focuses on exploration of the applicability of realized measures in volatility modeling and forecasting. We provide a first comprehensive study of jump variation impact on future volatility of Central and Eastern European stock markets. As a main workhorse, the recently proposed Realized Jump GARCH model, which enables a study of the impact of jump variation on future volatility forecasts, is used. In addition, we estimate Realized GARCH and heterogeneous autoregressive (HAR) models using one-minute and five-minute high frequency data. We find that jumps are important for future volatility, but only to a limited extent due to the high level of information aggregation within the stock market index. Moreover, Realized (Jump) GARCH models outperform the standard GARCH model in terms of data fit and forecasting performance. Comparison of forecasts with HAR models reveals that Realized (Jump) GARCH models capture higher portion of volatility variation. Eventually, Realized Jump GARCH compared to other Realized GARCH models provides comparable or even better forecasting performance.

Neste trabalho, visamos mostrar as características usuais dos dados de alta frequência, bem como utilizar modelagem não paramétrica para estimar a variância/volatilidade para esses dados. Após uma revisão sobre microestrutura de mercado, sazonalidade intradiária, variação quadrática e saltos, utilizamos os dados da PETR4 para estimar a variância realizada e variação bipotente. Determinadas essas séries, testamos se há saltos nas mesmas. Em seguida, analisamos o impacto que a microestrutura de mercado e a sazonalidade intradiária causam na detecção dos saltos. Concluímos que, enquanto a presença de microestrutura aponta para um número de saltos menor que o esperado, a sazonalidade intradiária aponta para o lado contrário, ou seja, ela causa um viés para detectar mais saltos, dada a estrutura típica da curva de volatilidade ao longo do dia em formato de J invertido, causando mais saltos incorretamente detectados no período mais volátil do dia (que corresponde a abertura da bolsa de valores). / In this work, we aim to show the usual characteristics of high-frequency data and the estimation of variance/volatility for this kind of data using nonparametric models. After reviewing concepts about market microstructure, intraday seasonality, quadratic variation and jumps, we use PETR4 data to estimate realized variance and bipower variation. With these series determined, we test for jumps. Then, we analyze the impact that market microstructure and intraday seasonality causes in jump detection. We conclude that while microstructure noise indicates fewer jumps than the ideal amount, intraday seasonality goes in the opposite direction, i.e., it detects more jumps than it should, since the typical inverted-J-shaped intraday volatility pattern tends to incorrectly detect more jumps at the most volatile period (which is when stock markets start negotiations).

Neste trabalho, visamos mostrar as características usuais dos dados de alta frequência, bem como utilizar modelagem não paramétrica para estimar a variância/volatilidade para esses dados. Após uma revisão sobre microestrutura de mercado, sazonalidade intradiária, variação quadrática e saltos, utilizamos os dados da PETR4 para estimar a variância realizada e variação bipotente. Determinadas essas séries, testamos se há saltos nas mesmas. Em seguida, analisamos o impacto que a microestrutura de mercado e a sazonalidade intradiária causam na detecção dos saltos. Concluímos que, enquanto a presença de microestrutura aponta para um número de saltos menor que o esperado, a sazonalidade intradiária aponta para o lado contrário, ou seja, ela causa um viés para detectar mais saltos, dada a estrutura típica da curva de volatilidade ao longo do dia em formato de J invertido, causando mais saltos incorretamente detectados no período mais volátil do dia (que corresponde a abertura da bolsa de valores). / In this work, we aim to show the usual characteristics of high-frequency data and the estimation of variance/volatility for this kind of data using nonparametric models. After reviewing concepts about market microstructure, intraday seasonality, quadratic variation and jumps, we use PETR4 data to estimate realized variance and bipower variation. With these series determined, we test for jumps. Then, we analyze the impact that market microstructure and intraday seasonality causes in jump detection. We conclude that while microstructure noise indicates fewer jumps than the ideal amount, intraday seasonality goes in the opposite direction, i.e., it detects more jumps than it should, since the typical inverted-J-shaped intraday volatility pattern tends to incorrectly detect more jumps at the most volatile period (which is when stock markets start negotiations).

Neste trabalho, visamos mostrar as características usuais dos dados de alta frequência, bem como utilizar modelagem não paramétrica para estimar a variância/volatilidade para esses dados. Após uma revisão sobre microestrutura de mercado, sazonalidade intradiária, variação quadrática e saltos, utilizamos os dados da PETR4 para estimar a variância realizada e variação bipotente. Determinadas essas séries, testamos se há saltos nas mesmas. Em seguida, analisamos o impacto que a microestrutura de mercado e a sazonalidade intradiária causam na detecção dos saltos. Concluímos que, enquanto a presença de microestrutura aponta para um número de saltos menor que o esperado, a sazonalidade intradiária aponta para o lado contrário, ou seja, ela causa um viés para detectar mais saltos, dada a estrutura típica da curva de volatilidade ao longo do dia em formato de J invertido, causando mais saltos incorretamente detectados no período mais volátil do dia (que corresponde a abertura da bolsa de valores). / In this work, we aim to show the usual characteristics of high-frequency data and the estimation of variance/volatility for this kind of data using nonparametric models. After reviewing concepts about market microstructure, intraday seasonality, quadratic variation and jumps, we use PETR4 data to estimate realized variance and bipower variation. With these series determined, we test for jumps. Then, we analyze the impact that market microstructure and intraday seasonality causes in jump detection. We conclude that while microstructure noise indicates fewer jumps than the ideal amount, intraday seasonality goes in the opposite direction, i.e., it detects more jumps than it should, since the typical inverted-J-shaped intraday volatility pattern tends to incorrectly detect more jumps at the most volatile period (which is when stock markets start negotiations).

This thesis uses Heterogeneous Autoregressive models of Realized Volatility on five-minute data of three of the most liquid financial assets - S&P 500 Futures index, Euro FX and Light Crude NYMEX. The main contribution lies in the length of the datasets which span the time period of 25 years (13 years in case of Euro FX). Our aim is to show that decomposing realized variance into continuous and jump components improves the predicatability of RV also on extremely long high frequency datasets. The main goal is to investigate the dynamics of the HAR model parameters in time. Also, we examine if volatilities of various assets behave differently. The results reveal that decomposing RV into its components indeed im- proves the modeling and forecasting of volatility on all datasets. However, we found that forecasts are best when based on short, 1-2 years, pre-forecast periods due to high dynamics of HAR model's parameters in time. This dynamics is revealed also by a year-by-year estimation on all datasets. Con- sequently, we consider HAR models to be inapproppriate for modeling RV on such long datasets as they are not able to capture the dynamics of RV. This was indicated on all three datasets, thus, we conclude that volatility behaves similarly for different types of assets with similar liquidity. 1

In this study, we show that realized bipower variation which is an extension of realized power variation is an alternative method that estimates integrated variance like realized variance. It is seen that realized bipower variation is robust to rare jumps. Robustness means that if we add rare jumps to a stochastic volatility process, realized bipower variation process continues to estimate integrated variance although realized variance estimates integrated variance plus the quadratic variation of the jump component. This robustness is crucial since it separates the discontinuous component of quadratic variation which comes from the jump part of the logarithmic price process. Thus, we demonstrate that if the logarithmic price process is in the class of stochastic volatility plus rare jumps processes then the difference between realized variance and realized bipower variation process estimates the discontinuous component of the quadratic variation. So, quadratic variation of the jump component can be estimated and jump detection can be achieved.

This thesis will investigate if adding an exogenous variable (implied volatility) to the variance equation will increase the performance for the GARCH(1,1) and EGARCH(1,1) models based on the OMXS30 index. These models are also compared with the implied volatility itself as a forecasting/modeling method. To evaluate the models the realized variance will be used as an unbiased estimator of the conditional variance. The findings suggest that adding implied volatility to the variance equation increase the overall performance.

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