The thesis deals with modeling and forecasting of natural gas spot prices, con- sumption of natural gas and average daily temperature. We assume that these three variables are influenced by each other, because as temperature decreases, consumption increases, which in turn increases the price with the increasing de- mand. Therefore, we propose to model these variables by vector autoregression. We compare this model with one-dimensional models where for each one we build a model from the ARMA-GARCH class. Models are estimated using historic va- lues and then designed models are used to simulate scenarios. Analysis of scenarios provides information to gas supply companies estimates of portfolio consumption and financial flows related to the purchase concerning natural gas. 1

This master thesis deals with the modeling of multivariate volatility in finan- cial time series. The aim of this work is to describe in detail selected approaches to modeling multivariate financial volatility, including verification of models, and then apply them in an empirical study of asset portfolio optimization. The results are compared with the classical approach of portfolio optimization theory based on unconditional moment estimates. The evaluation was based on four known op- timization problems, namely minimization of variance, Markowitz's model, ma- ximization of the Sharpe ratio and minimization of CVaR. The output portfolios were compared by using four metrics that reflect the returns and risks of the port- folios. The results demonstrated that employing the multivariate volatility models one obtains higher expected returns with less expected risk when comparing with the classical approach. 1

Made available in DSpace on 2015-05-08T14:45:02Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1380257 bytes, checksum: 1a02e73b7e0ca49d2f010e7b6925950a (MD5) Previous issue date: 2010-04-23 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This dissertation has as objective to estimate the relationship between monetary policy and the volatility of asset prices using the model BEKK, from January 2003 to October 2009. The specific objectives were: a) model the volatility of the Bovespa Index (Bovespa) and the Selic, referring to the money and stock through GARCH models, b) verify the clustering of volatility, the presence of persistent shocks and perform the analysis half-life in the financial market variables, c) estimate Vector Autoregressive models with the aim of testing the causal relationships in the sense of Granger (Granger Causality) between the transmission mechanism of monetary policy (interest rates) and the index stock; To achieve these objectives we used the model proposed by Bernanke, Gertler (1999, 2000) to describe the effects of volatility in monetary policy rules, and to capture the effects of volatility in monetary policy decisions were used in models family univariate and multivariate GARCH. The test of Granger causality show that there is unidirectional causality Ibovespa Selic regarding the period of greater volatility in the stock market (2003 - 2008), indicating that the returns in the stock market affected the Brazilian monetary policy decisions in this period . The estimation of GARCH models TARCHI and noted the existence of agglomeration of the variance, the effect of leverage on volatility and persistence on the part of stock markets and money. Through the model BEKKER is possible to highlight the volatility of the Selic rate is positively affected by common shocks and their lags inflation volatility, the volatility of the Bovespa index had a direct relationship with the volatility of the Selic rate in the period (2003 - 2008). This fact is consistent with the effects of movements in asset prices on aggregate demand, thus suggesting that policymakers are responding to changes in the market to avoid possible negative impacts on the economy. / Esta dissertação tem como objetivo estimar a relação entre a política monetária e a volatilidade dos preços dos ativos por meio do modelo BEKK, no período de janeiro de 2003 a outubro de 2009. Os objetivos específicos foram: a) modelar a volatilidade do Índice Bovespa (Ibovespa) e da Selic, referentes aos mercados monetário e acionário, por meio de modelos GARCH; b) verificar a aglomeração de volatilidade, presença da persistência dos choques e realizar a análise da meia-vida nas variáveis de mercado financeiro; c) estimar modelos Vetor Autoregressivo com o intuito de testar as relações de causalidade, no sentido de Granger (Granger Causality), entre o mecanismo de transmissão de política monetária (taxa de juros) e o índice acionário; Para atingir tais objetivos foi utilizado o modelo teórico proposto por Bernanke, Gertler (1999, 2000), para descrever os efeitos da volatilidade nas regras de política monetária, e para capturar os efeitos dessa volatilidade nas decisões de política monetária foram utilizados os modelos da família GARCH univariados e multivariados. O resultado do teste de causalidade de Granger mostrou que há causalidade unidirecional do Ibovespa em relação à Selic no período de maior volatilidade no mercado acionário (2003 - 2008), indicando que os retornos no mercado de ações brasileiros afetaram as decisões de política monetária nesse período. A estimação dos modelos TARCH e GARCH apontou a existência de aglomeração da variância, o efeito leverage e a persistência na volatilidade por parte dos mercados de ações e monetário. Por meio do modelo BEKK é possível destacar que a volatilidade da Selic é afetada positivamente por choques comuns as suas defasagens e a volatilidade da inflação; a volatilidade do Ibovespa apresentou uma relação direta com a volatilidade da taxa Selic no período (2003 - 2008). Esse fato é condizente com os efeitos dos movimentos nos preços dos ativos sobre a demanda agregada, sugerindo, portanto, que os policymakers estão reagindo às variações no mercado para evitarem possíveis impactos negativos sobre a economia.

本研究主要探討台灣各類股在不同貨幣單位之下，風險報酬之間的抵換關係，以此來探討台灣各類股在面對風險情況下的特性。我們考慮的有市場風險與國家特殊風險的影響，其中市場風險為整體經濟情勢帶來的風險；而國家風險代表一個地區的獨有風險，像是政治、經濟、社會等因素所帶來的風險。在衡量風險報酬抵換關係方面，我們藉由資本資產訂價模型的概念來做實證研究，並且藉由對角BEKK模型來做報酬與風險的條件共變異數的估計。我們先估計出市場風險與報酬之間的關係，爾後再加入國家風險因子的影響，並比較在不同貨幣單位之下的估計結果，而此結果亦能代表匯率風險的影響。 實證結果顯示，各大類股在面對風險的反應不一致，其中金融類股為受風險影響最大的類股，且其市場風險係數為顯著的負值，跟理論上風險報酬為正向關係不同。而其他類股在風險與報酬關係上，有正也有負向的結果出現，故我們可得知在面對相同風險之下，各類股有其不同的反應，且在不同的貨幣單位下得到的結果也有所差異，表示匯率的確會對風險報酬關係造成影響，甚至讓風險係數從負值轉為正值，故也顯示了匯率風險的存在。研究也顯示了國家風險對於各類股的影響係數皆不大，表示台灣地區的風險尚屬穩定。而本研究或許可幫助投資人在面對風險時，能藉由各類股風險報酬關係的反應來選擇最適的投資組合。 / This study investigates the various types of stock in Taiwan under the different monetary unit, between risk and return trade-off relations, in order to investigate the characteristics of various types of shares in Taiwan in the face of risk situations. We consider the impact of market risk and country-special risk, the risks of market risk for the economic situation; country risk represents a country risk, the risks such as political, economic, social and other factors . We have empirical research done by the concept of the capital asset pricing model, and the conditions covariance estimated by the diagonal BEKK model.We first estimate the relationship between market risk , and then add the impact of country risk factors, and compare the estimation results under different monetary unit, and this results in representing the exchange-rate risk. The empirical results show that the various stocks in the face of risk response is inconsistent, which financial stocks for the greatest impact on stocks are subject to risks, and the market risk coefficient is significantly negative, difference the theory. Other stocks in the relationship between risk and returns, positive and negative results, so we can learn to face the same risks under various types of shares have different reactions, and in a different currency unit the results also different, it also shows the existence of exchange-rate risk. The study also shows the country risk coefficient of various types of shares were weak effects. This research to help investors in the face of risk, by the reactions of all kinds shares the risk and return relationship to select the optimal portfolio.

In this thesis we study the regional and global linkages as evidence of markets integration of the stock markets in Frankfurt, Amsterdam, Prague the U.S. and the dynamics of volatility transmission of related foreign exchange rates using multivariate GARCH approach. For each of the model classes, a theoretical review, basic properties and estimation procedure are provided. We illustrate approach by applying the models to daily market data. Our two main aims are discussing and report the existence of regional and global stock markets linkages and provide comparison of such multivariate GARCH models on the data sample. We find out that the estimated time-varying conditional correlations indicate limited integration among the markets which implies that investors can benefit from the risk reduction by investigating in the different stock markets especially during the crisis.

The aim of this thesis is to assess the effect of ECB's communication on financial market co- movements between Italy, Spain, Germany and France using MGARCH family of models. Author addresses partially the potential problem of endogeneity of central bank communication by using Composite indicator of systemic stress and excess liquidity. The author estimates the impact of ECB's communication on correlations of government bond yield changes using daily data from 2008 to 2014. For this purpose author employs bivariate diagonal BEKK(1,1) and bivariate scalar BEKK(1,1) with surprises of macroeconomic announcements under control. The results are consistent and robust for all models, the results suggest that communication does not have statistically significant effect on financial market correlations in the Euro area. Furthermore, author defines delta functions which describe and quantify the immediate and full effect of explanatory variables on conditional correlations in bivariate diagonal BEKK(1,1) and bivariate scalar BEKK(1,1). To the best of author's knowledge this thesis is the only one in the literature which examines this effect of ECB's communication by MGARCH models. Keywords: Financial markets, central bank communication, correlation, MGARCH, BEKK Author's e-mail: milankucera1@seznam.cz...

The purpose of this study was to investigate the relationship between gold and stock returns with evidence from BRIC countries during 2001-2010. The importance of this topic is caused by instability in the world economy and stock markets, and due to this instability, there is a growing interest in gold from investors and the current bull market of gold. Considering that gold is independent from most of the macroeconomic factors we believe that it therefore should be independent from or low correlated with stock, which makes this metal useful for portfolio diversification. Based on previous studies, we also believe that gold can be used to predict, to some degree, the stock market trend. The force behind such stable price growth of gold is sustained by demand from emerging countries such as BRICs. Moreover, there is lack of research on this topic from the perspective of different economic sectors. These facts determined the choice of countries along with their economic sectors. The research was designed in the frame of quantitative method. The types of relationship that were investigated are correlation and spillover effects. In order to examine these relationships we have utilized secondary data, which are gold prices and stock indices turned into returns. The Pearson’s correlation and diagonal BEKK GARCH were applied to test the correlation and spillover effects between returns of gold and stock, respectively. The results of the study showed that gold and stock returns are correlated, however to a low degree. Additionally, correlation varies across countries and their economic sectors over time, which may influence investors’ decision in choice of allocation of investments. The other findings showed the existence of mean spillover effects, both unidirectional and bidirectional, and volatility spillover effects between gold and stock returns. The principal conclusions were that gold is an efficient portfolio diversifier, which also plays a role of a hedge and a safe haven. Similarly, taking into account an existence of spillover effects, gold can be helpful in terms of stock prediction and vice versa. Further, another important finding was that not all of the economic sectors had mean spillover with gold, but in terms of volatility, every sector had a certain relationship with gold.

This dissertation investigates the volatility of the relationships between exchange rates and interest rates. The first part of the paper explores the transmission relationship between these two markets using a time-series model. Previous studies have assumed that covariance was constant in both markets. However, if the volatilities of the exchange rate and interest rate markets are correlated over time, the interaction and spillover effects between the two markets may be affected by time-varying covariance. Hence, this paper utilizes the BEKK-GARCH model developed by Engle and Kroner (1995) to capture the dynamic relationship between the exchange rates and interest rates. This study uses the returns data for G7 members¡¦ exchange rates and interest rates to test whether these markets exhibited volatilities spillover from 1978 to 2009. The results show bi-directional volatility spillovers in the markets of the UK, the Euro countries, and Canada, where the volatilities of the two markets were interrelated. The second part of the paper explores the relationship between exchange rates and interest rates using a jump diffusion model. Previous studies assumed that the dynamic processes of exchange rates and interest rates follow a diffusion process with a continuous time path, but an increasing number of empirical studies have shown that a continuous diffusion stochastic model does not capture the dynamic process of these variables. Thus, this paper investigates the discontinuous variables of exchange rates and interest rates and assumes that these variables follow a jump diffusion process. The UIRP model is employed to explore the relationship between both variables and to divide the systematic risk into systematic continuous risk and systematic jump risk. The returns data for G7 members¡¦ exchange rates and interest rates from 2005 to 2010 were analyzed to test whether the expected exchange rate is affected by jump components when the interest rate market experiences a jump. The results show that the jump diffusion model has more explanatory power than the pure diffusion model does, and, when the interest rate market experiences a jump risk, the systematic jump risk has a significant relationship with the expected exchange rates in some G7 countries.

近年來由於市場型式為開放主體，在財務整合，商品區隔的環境下，投資人在進行投資時，應考量全方面的訊息，亦即國家內外部所有會影響股票市場的風險因子。而風險與報酬之間是否存在抵換關係，一直以來皆為備受討論的議題，從過去的文獻當中，研究者多以變異數作為衡量風險的代理，再透過各種不同的研究方法來估計風險報酬係數，但實證上並未獲得一致的結果。本文以1981年1月至2008年7月為研究期間，台灣與韓國之股價指數月資料為樣本，所使用之模型參考Turan G. Bali & Liuren Wu(2010)的研究論文，利用簡化過後的雙變量BEKK-GARCH(1，1)模型進行估計，探討台灣與韓國股票市場跨期收益與風險之關係。本文主要分為三大部分，首先先將台灣及韓國的股價指數以美元計價，針對全球市場觀察其風險以及持續性，並且利用共變異數來判別兩國股市分別為高風險或是低風險，再者，將台灣及韓國的股價指數分別以自己國家之幣別計算，將計算出之殘差估計個別國家股市風險，看是否兩國家內部的非經濟因素，例如:政治及軍事等，會影響股市的表現。最後一部份為前兩部分的整合，比較個別國家風險與全球市場風險對台灣及韓國股市的影響以及超額報酬與風險之間的抵換關係。實證結果顯示，不論就台灣或者是韓國而言，全球市場風險的風險與報酬係數皆為正向顯著，其中又以台灣之係數較為高，透露出若在承擔相同的全球市場風險時，台灣的投資人會較韓國的投資人要求較高的報酬。在匯率風險方面，本文採Turan G. Bali & Liuren Wu(2010)所使用的研究方法，將風險與報酬的抵換關係建立在不同國家的幣別之下進行估計，由結果發現，若以美元為單位來衡量風險報酬係數，則不論是台灣或韓國，在全球市場風險下，係數皆較小；若以個別貨幣來衡量，其台灣的風險與報酬抵換係數較大，韓國之係數則是由正值轉變為負值，代表匯率的確會對市場風險值有所影響，匯率風險是可以被定價的。 / In recent years, due to the opening of the markets, there are more and more choices in the investments. Investors should consider all aspects of information in this world with financial market integration but goods market segmentation. The intertemporal relation between risk and return in the stock market has been one of the most extensively studied topics in financial economics. The risk-return coefficients across different currency denomination change when considering different specification for the conditional covariance process. We used the bivariate BEKK-GARCH (1,1) model as the basic used in the reference by Turan G. Bali & Liuren Wu (2010) estimating the risk-return coefficients and measuring how this risk aversion estimate varies with different currency denominations. We started our analysis using monthly data from January 1981 to July 2008 on the Standard & Poor's 500 index, Taiwan stock exchange corporation and Korea composite stock price index. This article was divided into three parts. First, we computed monthly returns on the indices based on U.S. dollar denomination and calculated the excess returns as the index return minus the short-term interest rate. Second, we estimated the conditional covariances between the excess returns on the world market portfolio and the excess returns on two country indices using a bivariate GARCH specification. Third, we estimated the common relation of the equations implied by the international version of the intertemporal capital asset pricing model between the expected excess returns on those two country indices and the corresponding conditional covariances. After repeating the above procedure and estimating the intertemporal risk-return relation under different currency denomination, the empirical results showed that the risk-return coefficients in the world market portfolio was significantly positive in Taiwan and Korea. We also found that the coefficient was different based on different currency denominations on behalf of the exchange rate risk can be priced.

A crise financeira americana de 2008 acarretou alta na volatilidade na maioria das bolsas de valores mundo afora. Nesse trabalho, é testada e analisada a hipótese de contágio financeiro como mecanismo de transmissão da crise iniciada em 2008 dos Estados Unidos para 16 países da amostra. Por meio de modelos multivariados de volatilidade das classes BEKK e DCC e testes de quebras estruturais, conclui-se que a hipótese de contágio financeiro é verificada em todos os países estudados para justificar a alta acima do esperado das volatilidades dos mercados durante os anos de crise. Também é verificado que países apresentam diferentes graus de exposição ao risco de contágio, de acordo com nível de abertura de suas economias e participação de investimento externo em seus mercados financeiros. / The 2008 American financial crisis caused high volatility in most stock markets worldwide. In this study, it is tested and analyzed the hypothesis of financial contagion as a mechanism of transmission for the crisis beginning in 2008 in United States to the 16 countries in the sample. Using multivariate BEKK and DCC volatility models, and tests of structural breakpoints, it is concluded that the hypothesis of financial contagion is verified in all countries studied to justify volatility higher than expected in the markets during the crisis years. It is also noted that countries have different degrees of exposure to contagion, according to level of economic openness and foreign investment participation in their financial markets.