MASTER THESIS MODELLING AND COMPARATIVE ANALYZES OF VOLATILITY SPILLOVER BETWEEN US, CZECH REPUBLIC AND SERBIAN STOCK MARKETS Abstract This paper estimates Serbian, Czech and US stock markets volatility. Few studies analyzed stock market linkages for these three markets. The mean equation is estimated using the vector auto- regression model. The second moments is further estimated using different multivariate GARCH models. We find that current conditional volatilities for each stock is highly affected by the past innovations. Cross-market correlations are significant as well. However, there is a higher conditional correlation between Czech and US stock market indices compared to the conditional correlation between Serbian and US stock indices.

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.

Made available in DSpace on 2016-04-25T16:44:46Z (GMT). No. of bitstreams: 1 Paulo Renato Marchese Garcia.pdf: 1597436 bytes, checksum: b8aeae0fcbfaf4d72d7899cc1060414d (MD5) Previous issue date: 2015-02-26 / This study aims to empirically test the model of the conditional CAPM in the Brazilian stock market. The analysis is developed through theoretical exposition of the main causes that built the capital asset pricing model and the conditions under which it has been tested and developed. For this purpose, we used a sample of financial assets extracted from Economática system. After that six portfolios were formed based on financial literature assumptions in order to calculate the excess of return in each case. Following the procedure an econometric model was tested and adjusted to be possible its application apply the CAPM conditional version into Brazilian stocks market. Finally, the process was validated given the metrics presented in econometric results being robust and corroborating with the literature / Este trabalho tem por objetivo testar empiricamente o modelo do CAPM condicional no mercado acionário brasileiro. A análise é desenvolvida através da exposição teórica das principais causas que proporcionaram o surgimento do modelo de precificação de ativos financeiros e as condições nas quais ele foi testado e desenvolvido. Para tal, foi utilizada uma amostra de ativos financeiros extraídas do sistema Economática e com base na literatura foram formadas carteiras a fim de calcular o excesso de retorno das composições.Com base em testes econométricos e ajuste da modelagem foi possível aplicar o CAPM condicional no mercado acionário brasileiro e validar sua aplicação uma vez que as métricas apresentadas nos resultados econométricos mostraram-se robustas corroborando com a literatura

The aim of the thesis is to identify an appropriate model in forecasting Value-at-Risk on a morevolatile period than that one from which the model is estimated. We estimate 1-day-ahead and10-days-ahead Value-at-Risk on a number of exchange rates. The Value-at-Risk estimates arebased on three models combined with three distributional assumptions of the innovations, andthe evaluations are made with Kupiec's (1995) test for unconditional coverage. The data rangesfrom January 1st 2006 through June 30th 2011. The results suggest that the GARCH(1,1) andGJR-GARCH(1,1) with normally distributed innovations are models adequately capturing theconditional variance in the series.

This thesis is focused on local polynomial smoothers of the conditional vari- ance function in a heteroscedastic nonparametric regression model. Both mean and variance functions are assumed to be smooth, but neither is assumed to be in a parametric family. The basic idea is to apply a local linear regression to squa- red residuals. This method, as we have shown, has high minimax efficiency and it is fully adaptive to the unknown conditional mean function. However, the local linear estimator may give negative values in finite samples which makes variance estimation impossible. Hence Xu and Phillips proposed a new variance estimator that is asymptotically equivalent to the local linear estimator for interior points but is guaranteed to be non-negative. We also established asymptotic results of both estimators for boundary points and proved better asymptotic behavior of the local linear estimator. That motivated us to propose a modification of the local li- near estimator that guarantees non-negativity. Finally, simulations are conducted to evaluate the finite sample performances of the mentioned estimators.

This thesis examines the volatility forecasting performance of six commonly used forecasting models; the simple moving average, the exponentially weighted moving average, the ARCH model, the GARCH model, the EGARCH model and the GJR-GARCH model. The dataset used in this report are three different Nordic equity indices, OMXS30, OMXC20 and OMXH25. The objective of this paper is to compare the volatility models in terms of the in-sample and out-of-sample fit. The results were very mixed. In terms of the in-sample fit, the result was clear and unequivocally implied that assuming a heavier tailed error distribution than the normal distribution and modeling the conditional mean significantly improves the fit. Moreover a main conclusion is that yes, the more complex models do provide a better in-sample fit than the more parsimonious models. However in terms of the out-of-sample forecasting performance the result was inconclusive. There is not a single volatility model that is preferred based on all the loss functions. An important finding is however not only that the ranking differs when using different loss functions but how dramatically it can differ. This illuminates the importance of choosing an adequate loss function for the intended purpose of the forecast. Moreover it is not necessarily the model with the best in-sample fit that produces the best out-of-sample forecast. Since the out-of-sample forecast performance is so vital to the objective of the analysis one can question whether the in-sample fit should even be used at all to support the choice of a specific volatility model.

O objetivo deste trabalho é apresentar e comparar diferentes métodos de modelagem da volatilidade (variância condicional) de séries temporais financeiras. O modelo ARFIMA é empregado para capturar o comportamento de memória longa observado na volatilidade de séries financeiras. Por sua vez, o modelo GARCH é utilizado para modelar a volatilidade variando no tempo destas séries. Finalmente, o modelo FIGARCH é utilizado para modelar a dinâmica dos retornos de séries temporais financeiras juntamente com sua volatilidade. Serão apresentados alguns estimadores para os parâmetros dos modelos estudados. Foram realizadas simulações dos três tipos de modelos com o objetivo de comparar o comportamento dos estimadores para diferentes valores dos parâmetros. Por fim, serão apresentadas aplicações em séries reais. / The goal of this project is to present and compare differents methods of modeling volatility (conditional variance) in financial time series. ARFIMA model is applied to capture long memory behavior of volatility in financial time series. GARCH model is used to model the temporal variation in financial volatility. Finally, FIGARCH model is used to model dynamic of financial time series returns as well as its volatility behavior. We present some estimators for the studied models. Estimators behavior of the three types of models for different parameters is assessed through a simulation study. At last, applications to real data are presented.

O objetivo deste trabalho é apresentar e comparar diferentes métodos de modelagem da volatilidade (variância condicional) de séries temporais financeiras. O modelo ARFIMA é empregado para capturar o comportamento de memória longa observado na volatilidade de séries financeiras. Por sua vez, o modelo GARCH é utilizado para modelar a volatilidade variando no tempo destas séries. Finalmente, o modelo FIGARCH é utilizado para modelar a dinâmica dos retornos de séries temporais financeiras juntamente com sua volatilidade. Serão apresentados alguns estimadores para os parâmetros dos modelos estudados. Foram realizadas simulações dos três tipos de modelos com o objetivo de comparar o comportamento dos estimadores para diferentes valores dos parâmetros. Por fim, serão apresentadas aplicações em séries reais. / The goal of this project is to present and compare differents methods of modeling volatility (conditional variance) in financial time series. ARFIMA model is applied to capture long memory behavior of volatility in financial time series. GARCH model is used to model the temporal variation in financial volatility. Finally, FIGARCH model is used to model dynamic of financial time series returns as well as its volatility behavior. We present some estimators for the studied models. Estimators behavior of the three types of models for different parameters is assessed through a simulation study. At last, applications to real data are presented.

This thesis consists of four research papers. The main focus is on building the multivariate Conditional Correlation (CC-) GARCH models. In particular, emphasis lies on considering an extension of CC-GARCH models that allow for interactions or causality in conditional variances. In the first three chapters, misspecification testing and parameter restrictions in these models are discussed. In the final chapter, a computer package for building major variants of the CC-GARCH models is presented. The first chapter contains a brief introduction to the CC-GARCH models as well as a summary of each research paper. The second chapter proposes a misspecification test for modelling of the conditional variance part of the Extended Constant CC-GARCH model. The test is designed for testing the hypothesis of no interactions in the conditional variances. If the null hypothesis is true, then the conditional variances may be described by the standard CCC-GARCH model. The test is constructed on the Lagrange Multiplier (LM) principle that only requires the estimation of the null model. Although the test is derived under the assumption of the constant conditional correlation, the simulation experiments suggest that the test is also applicable to building CC-GARCH models with changing conditional correlations. There is no asymptotic theory available for these models, which is why simulation of the test statistic in this situation has been necessary. The third chapter provides yet another misspecification test for modelling of the conditional variance component of the CC-GARCH models, whose parameters are often estimated in two steps. The estimator obtained through these two steps is a two-stage quasi-maximum likelihood estimator (2SQMLE). Taking advantage of the asymptotic results for 2SQMLE, the test considered in this chapter is formulated using the LM principle, which requires only the estimation of univariate GARCH models. It is also shown that the test statistic may be computed by using an auxiliary regression. A robust version of the new test is available through another auxiliary regression. All of this amounts to a substantial simplification in computations compared with the test proposed in the second chapter. The simulation experiments show that, under both under both Gaussian and leptokurtic innovations, as well as under changing conditional correlations, the new test has reasonable size and power properties. When modelling the conditional variance, it is necessary to keep the sequence of conditional covariance matrices positive definite almost surely for any time horizon. In the fourth chapter it is demonstrated that under certain conditions some of the parameters of the model can take negative values while the conditional covariance matrix remains positive definite almost surely. It is also shown that even in the simplest first-order vector GARCH representation, the relevant parameter space can contain negative values for some parameters, which is not possible in the univariate model. This finding makes it possible to incorporate negative volatility spillovers into the CC-GARCH framework. Many new GARCH models and misspecification testing procedures have been recently proposed in the literature. When it comes to applying these models or tests, however, there do not seem to exist many options for the users to choose from other than creating their own computer programmes. This is especially the case when one wants to apply a multivariate GARCH model. The last chapter of the thesis offers a remedy to this situation by providing a workable environment for building CC-GARCH models. The package is open source, freely available on the Internet, and designed for use in the open source statistical environment R. With this package can estimate major variants of CC-GARCH models as well as simulate data from the CC-GARCH data generating processes with multivariate normal or Student's t innovations. In addition, the package is equipped with the necessary functions for conducting diagnostic tests such as those discussed in the third chapter of this thesis. / <p>Diss. Stockholm : Handelshögskolan, 2010. Sammanfattning jämte 4 uppsatser.</p>

Submitted by HELENO PIAZENTINI VIEIRA (helenopv@gmail.com) on 2014-05-09T14:03:11Z No. of bitstreams: 1 Velocidade da moeda, inflação e ciclos de negócios no Brasil, 1900-2013.pdf: 1362534 bytes, checksum: 0cbd1b1891b345cdf3b1487cd6c24344 (MD5) / Approved for entry into archive by Suzinei Teles Garcia Garcia (suzinei.garcia@fgv.br) on 2014-05-09T17:51:44Z (GMT) No. of bitstreams: 1 Velocidade da moeda, inflação e ciclos de negócios no Brasil, 1900-2013.pdf: 1362534 bytes, checksum: 0cbd1b1891b345cdf3b1487cd6c24344 (MD5) / Made available in DSpace on 2014-05-09T19:40:39Z (GMT). No. of bitstreams: 1 Velocidade da moeda, inflação e ciclos de negócios no Brasil, 1900-2013.pdf: 1362534 bytes, checksum: 0cbd1b1891b345cdf3b1487cd6c24344 (MD5) Previous issue date: 2014-04-22 / A presente tese é composta por três ensaios. O primeiro ensaio estuda os ciclos de negócios brasileiro no período dos anos 1900 até 2012. Uma série trimestral do PIB real é elaborada, utilizando um modelo estrutural de séries de tempo. A partir disso, um modelo com mudança Markoviana é proposto para que seja construída uma cronologia de ciclo de negócios. O modelo selecionado possui dois regimes distintos, cenários de expansão e de recessão, a datação obtida é comparada com outros estudos sobre o tema e são propostas caracterizações das fases de crescimento que podem apoiar estudos sobre a história econômica do Brasil. O segundo ensaio estuda o comportamento da velocidade da moeda no ciclo de negócios brasileiro de 1900 até 2013. Os resultados a partir das estimativas dos modelos de séries temporais, MS e GARCH, são utilizados para suportar esse estudo. Em termos gerais a velocidade da moeda no Brasil apresentou queda até a segunda Guerra Mundial, cresceu até meados dos anos 1990 e a partir disso segue em tendência de queda. A experiência inflacionária brasileira é capítulo importante de nossa história econômica. O objetivo do terceiro ensaio é estudar a volatilidade da inflação brasileira ao longo do tempo no período de 1939 até 2013, buscando descrever sua relação com a taxa de inflação, adotando como referência uma datação de ciclos de negócios. Para realizar essa descrição serão utilizados os resultados obtidos nas estimações de modelos econométricos das classes GARCH, BSM e MS. No caso brasileiro a indicação é que a taxa de inflação impacta positivamente sua volatilidade. / This doctoral thesis is composed by three essays. The first one studies the Brazilian business cycles during the years 1900 to 2012. A quarterly real GDP measure is produced using a structural model of time series. For this, Markov Switching model is proposed to be constructed a chronology of business cycle. The selected model has two distinct regimes scenarios of expansion and recession, the dating obtained is compared with other studies on the subject are proposed characterizations and the stages of growth that can support studies on the economic history of Brazil. The second paper studies the behavior of the velocity of money in the Brazilian business cycle from 1900 to 2013. The results from the estimation of models for time series GARCH and MS, are used to support this study. In general the velocity of money in Brazil fell to the Second World War, has grown to the mid-1990s and from this follows on a downward trend. The Brazilian inflation experience is important chapter in our economic history. The objective of the third paper is to study the volatility of the Brazilian inflation over time in the period 1939 to 2013, trying to describe his relationship with the rate of inflation, taking as a reference dating of business cycles. To conduct this description the results obtained in the estimations of GARCH, MS and BSM models classes will be used. In the Brazilian case the indication is that the inflation rate positively impacts the volatility of this variable.