This volume contains four essays on various topics in the field of financial econometrics. All four discuss the properties of high frequency financial data and its implications on the model choice when an estimate of the capital asset return volatility is in focus. The interest lies both in characterizing "stylized facts" in such series with time series models and in predicting volatility. The first essay, entitled A Survey of Recent Papers Considering the Standard &amp; Poor 500 Composite Stock Index, presents recent empirical findings and stylized facts in the financial market from 1987 to 1996 and gives a brief introduction to the research field of capital asset return volatitlity models and properties of high frequency financial data. As the title indicates, the survey is restricted to research on the well known Standard &amp; Poor 500 index. The second essay, with the title, Stylized Facts of Daily Return Series and the Hidden Markov Model, investigates the properties of the hidden Markov Model, HMM, and its capability of reproducing stylized facts of financial high frequency data. The third essay, Modelling the Conditional Mean and Conditional Variance: A combined Smooth Transition and Hidden Markov Approach with an Application to High Frequency Series, investigates the consequences of combining a nonlinear parameterized conditional mean with an HMM for the conditional variance when characterization of stylized facts is considered. Finally, the fourth essay entitled, Volatility Forecasting for Option Pricing on Exchange Rates and Stock Prices, investigates the volatility forecasting performance of some of the most frequently used capital asset return volatility models such as the GARCH with normal and t-distributed errors, the EGARCH and the HMM. The prediction error minimization approach is also investigated. Each essay is self-contained and could, in principle, be read in any order chosen by the reader. This, however, requires a working knowledge of the properties of the HMM. For readers less familiar with the research field the first essay may serve as an helpful introduction to the following three essays. / <p>Diss. Stockholm : Handelshögsk.</p>

This thesis comprises four papers concerning risk prediction. Paper [I] suggests a nonlinear and multivariate time series model framework that enables the study of simultaneity in returns and in volatilities, as well as asymmetric effects arising from shocks. Using daily data 2000-2006 for the Baltic state stock exchanges and that of Moscow we find recursive structures with Riga directly depending in returns on Tallinn and Vilnius, and Tallinn on Vilnius. For volatilities both Riga and Vilnius depend on Tallinn. In addition, we find evidence of asymmetric effects of shocks arising in Moscow and in the Baltic states on both returns and volatilities. Paper [II] argues that the estimation error in Value at Risk predictors gives rise to underestimation of portfolio risk. A simple correction is proposed and in an empirical illustration it is found to be economically relevant. Paper [III] studies some approximation approaches to computing the Value at Risk and the Expected Shortfall for multiple period asset re- turns. Based on the result of a simulation experiment we conclude that among the approaches studied the one based on assuming a skewed t dis- tribution for the multiple period returns and that based on simulations were the best. We also found that the uncertainty due to the estimation error can be quite accurately estimated employing the delta method. In an empirical illustration we computed five day Value at Risk's for the S&amp;P 500 index. The approaches performed about equally well. Paper [IV] argues that the practise used in the valuation of the port- folio is important for the calculation of the Value at Risk. In particular, when liquidating a large portfolio the seller may not face horizontal de- mandcurves. We propose a partially new approach for incorporating this fact in the Value at Risk and in an empirical illustration we compare it to a competing approach. We find substantial differences.

In this paper the performance of classical approaches and GARCH family models are evaluated and compared in estimation one-step-ahead VaR. The classical VaR methodology includes historical simulation (HS), RiskMetrics, and unconditional approaches. The classical VaR methods, the four univariate and two multivariate GARCH models with the Student’s t and the normal error distributions have been applied to 5 stock indices and 4 portfolios to determine the best VaR method. We used four evaluation tests to assess the quality of VaR forecasts: -                     Violation ratio -                     Kupiec’s test -                     Christoffersen’s test -                     Joint test The results point out that GARCH-based models produce far more accurate forecasts for both individual and portfolio VaR. RiskMetrics gives reliable VaR predictions but it is still substantially inferior to GARCH models. The choice of an optimal GARCH model depends on the individual asset, and the best model can be different based on different empirical data.

This thesis focuses on stochastic processes and some of their properties are investigated which are necessary to determine the tools, the extremal index and the extremogram. Both mathematical tools measure extremal dependency within random time series. Two different models are introduced and related properties are discussed. The probability function of the Agent based model is surveyed explicitly and strong stationarity is proven. Data sets for both processes are simulated and clustering of the data is investigated with two different methods. Finally an estimation of the extremogram is used to interpret dependency of extremes within the data.

This paper examines the impact of USD and EUR exchange rates on the Swedish stock market performance for different economic sectors over a time period of ten years (2003-2013). The growing integration between foreign exchange markets and stock markets with the wide spread use of hedging and diversification policies made it necessary to test the degree of impact these two distinct markets share between each other. Number of studies, were done studying the relationship between the exchange rates and stock performance combining and comparing different economies and currencies. Nevertheless, research gap prevailed when it came at the point of the studying the relationship on Swedish stock and foreign exchange market. The research was conducted with the quantitative method. Initially we have tested how the performance of Swedish stock market is correlated with the return of the USD and EUR in different economic sectors over different time periods. Later, we try to investigate if there is any spillover effect flows from the exchange market to the Swedish stock market. The Pearson’s correlation coefficient and GARCH (1,1) model were applied to study the correlation and spillover effect between the exchange and stock return respectively. Our empirical study showed that there is very low correlation which is statistically insignificant between the two different markets. Correlations were found to be significantly varied across the different economic sectors in different time periods. Moreover empirical study supported that the spillover effect exists and showed that movement of exchange rates will affect the future performance of stock market. The significant conclusions were that USD and EUR can be used as portfolio diversification and during the volatile exchange market, investors should diversify or hedge their risk domestically and vice versa. The implications of this finding is particularly very important for the portfolio managers when devising their hedging policies and diversifying their portfolios in order to minimize their unsystematic risk.

La prévision de la volatilité future constitue l'un des principaux enjeux actuels dans la finance contemporaine. De ce fait, une estimation précise de la volatilité, seul paramètre inobservable sur le marché, est cruciale pour la prise de décision en allocation d'actifs et en gestion des risques. Les modèles GARCH se basent sur les cours boursiers passés pour calculer ou estimer la volatilité. L'hypothèse qui se cache derrière cette approche est que l'on peut se servir du passé pour prédire l'avenir. Les modèles GARCH semblent toutefois peu adaptés à la prévision à long terme puisqu'ils présentent un retour à la moyenne. Nous avons alors utilisé le modèle EWMA qui présente l'avantage de ne pas retourner à la moyenne et nous avons estimé les paramètres des modèles étudiés pour reconstruire une volatilité historique de l'indice S&P500 par le biais de chaque modèle afin de les comparer avec le modèle de la volatilité réalisée. Les résultats de notre recherche montrent que la volatilité estimée par le modèle GARCH de Heston et Nandi (2000) n'est pas en mesure de reproduire la trajectoire suivie par la volatilité de l'indice S&P500 et ce modèle ne pourrait donc être employé pour faire des prévisions sur celle-ci. Nous avons trouvé également que le modèle EWMA semble significativement reproduire la même trajectoire que celle associée à la volatilité réalisée de l'indice et par conséquent on peut l'utiliser pour prévoir la volatilité future de l'indice S&P500. ______________________________________________________________________________ MOTS-CLÉS DE L’AUTEUR : Volatilité, S&P500, GARCH, EWMA, Heston et Nandi, VIX.

The objective for this master thesis is to investigate the possibility to predict the risk of stocks in financial markets. The data used for model estimation has been gathered from different branches and different European countries. The four data series that are used in the estimation are price series from: Münchner Rück, Suez-Lyonnaise des Eaux, Volkswagen and OMX, a Swedish stock index. The risk prediction is done with univariate GARCH models. GARCH models are estimated and validated for these four data series. Conclusions are drawn regarding different GARCH models, their numbers of lags and distributions. The model that performs best, out-of-sample, is the APARCH model but the standard GARCH is also a good choice. The use of non-normal distributions is not clearly supported. The result from this master thesis could be used in option pricing, hedging strategies and portfolio selection.

The purpose of this thesis is to examine whether Swedish Equity L/S hedge funds present a lower market risk than the index S&amp;P Europe 350 over our holding period using a GARCH/EGARCH Value-at-Risk model. The sample consists of 96 monthly observa- tions between March 2004 and February 2012. The examination shows that the hedge funds in general hold a lower market risk than the index for the next holding period and al- so present a lower estimated loss if our VaR loss is exceeded. This implies that hedge funds would be a good choice for investors to have in a portfolio to reduce the risk.

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.

<p>In this paper, we propose a new learning algorithm for non-stationary Dynamic Bayesian Networks is proposed. Although a number of effective learning algorithms for non-stationary DBNs have previously been proposed and applied in Signal Pro- cessing and Computational Biology, those algorithms are based on batch learning algorithms that cannot be applied to online time-series data. Therefore, we propose a learning algorithm based on a Particle Filtering approach so that we can apply that algorithm to online time-series data. To evaluate our algorithm, we apply it to the simulated data set and the real-world financial data set. The result on the simulated data set shows that our algorithm performs accurately makes estimation and detects change. The result applying our algorithm to the real-world financial data set shows several features, which are suggested in previous research that also implies the effectiveness of our algorithm.</p> / Thesis