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.

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.

In this thesis the GARCH models are applied to evaluate financial options and futures. In the first application, the GARCH models in parsimonious form are studied for pricing the S&P500 options. Unlike previous studies that focus on developed formulation, the results indicate that simplified models provide effective performance and it is the simple GARCH model that yields the least valuation error. To our consideration, examining model possessing simplification is of practical importance because model estimation becomes readily accessible through available econometric software, which circumvent programming barriers in implementing alternative one’s own pricing methods. The second application consider the component GARCH models for currency option pricing. The valuation results favour the component formulations particularly in the pricing of long term contracts. Volatility modelling results indicate that the return-volatility relationship is symmetric in the long run, but over the short term asymmetry also arises in the EURUSD and GBPUSD exchange rates. The third application evaluates canola futures in Canada in relation to spot market price. Results confirm the cointegrating relationship with threshold corresponding to transaction and adjustment cost. And it is the futures market that adjusts actively to price disparities but in the meantime there is volatility spillover from futures to the spot market. Overall, our empirical assessments indicate the importance of the time varying volatility and the improvements achieved in option pricing and futures evaluation. We believe the present study’s analysis provides useful suggestions and further guidance to practitioners and investors for the pricing and trading in the equity and foreign exchange markets, also to the market agents to better evaluate price uncertainty in order to guard against adverse price changes.

Syfte: Syftet med den här studien var att undersöka följsamheten och reduktionen av det horisontella överbettet vid behandling med van Beek-aktivator genom att jämföra en rekommenderad användningstid av tolv och åtta timmar per dag. Material och metod: Tretton patienter (4 pojkar och 9 flickor) ingick i undersökningsmaterialet med en medelålder på 10,0 år (SD = 0,9). Alla patienter var diagnostiserade med en Angle Klass II-bettavvikelse och behandlades med van Beek-aktivator. Patienterna var randomiserade i två grupper med två olika användningstider (8 timmar och 12 timmar). Följsamheten mättes med hjälp av en mikrosensor (TheraMon®) inbyggd i aktivatorn och det horisontella och vertikala överbettet registrerades efter första, tredje och sjätte månaden. Efter att datan var insamlad gjordes statistisk analys för att påvisa ifall statistisk skillnad fanns mellan grupperna.Resultat: Medelreduceringen i horisontellt överbett i 8-timmarsgruppen var efter sex månader 3,4 mm jämfört med hos 12-timmarsgruppen som var 3,5 mm. Medelanvändningstiden var i 12-timmarsgruppen och 8-timmarsgruppen 8.2 timmar (SD=1,7) och 7,9 timmar (SD=2,6) per dag respektive. Den genomsnittliga användningstiden för samtliga patienter var 8,1 timmar.Slutsats: Rekommendation av åtta timmar var enklare att uppnå jämfört med tolv timmar. Van Beek-aktivatorn var effektiv för korrigering av Angle Klass II-bettavvikelser, ingen klinisk signifikant skillnad i behandlingseffekt observerades mellan de två grupperna. / Aim: The aim of this study was to evaluate the compliance and overjet changes among patients treated with the van Beek activator comparing a twelve- and eight-hours daily wear-time prescription. Material and methods: The study sample consisted of thirteen patients (4 boys and 9 girls) with a mean age of 10.0 years (SD = 0.9). All patients had a Class II malocclusion and were treated with the van Beek activator. Patients were randomly assigned to two groups with a wear-time of twelve and eight hours respectively. Compliance was measured with the aid of a microsensor (TheraMon®) built into the activator and the overjet and overbite were recorded after the first, third and sixth month. Results: The mean decrease in overjet among the 8 hours group after six months was 3.4 mm compared to the 3.5 mm overjet reduction recorded in the 12 hours group. The mean wear-time in the 12 hours group and 8 hours group were 8.2 hours (SD = 1.7) and 7.9 hours (SD = 2.6) per day respectively. The overall mean daily wear-time of all patients in both groups was 8.1 hours. Conclusions: The eight-hours prescription was easier to achieve compared to the twelve-hours. The van Beek activator was effective in Class II correction, no clinically significant difference in treatment effect was observed between the two wear-time prescriptions.

本研究主要探討次級房貸風暴前後美國、台灣與日本股市之間的關聯性，研究方法利用二元與三元BEKK模型，來檢視次級房貸風暴前後美國、台灣與日本股市之間訊息傳遞效果與波動外溢效果。實證結果顯示，比起日本股市，美國股市對台灣股市影響較大。而比起二元模型，三元模型結果較為合理，在次級房貸風暴發生前，美國股市衝擊單向影響台灣非金融類股，而日本股市對台灣加權指數也存在單向的訊息傳遞效果，風暴發生期間，三國股市之間未存在明顯關係，但在風暴發生後，美國股市衝擊轉而影響台灣加權指數與台灣金融類股，其股市波動也影響著台灣加權指數。

This master thesis deals with extension of the univariate GARCH model to multivari- ate models. We present individual models and deal with methods of their estimation. Then we describe some statistical tests for diagnosting the models. We have programmed in the statistical software R one of them - the Ling-Li test. Afterwards we apply selected models to real data of stock market index S&P 500, stock market index Russell 2000 and stocks of crude oil. For the GO-GARCH model, we compare all available estimation methods and show their differences. Then we compare the results of all models with each other and also with univariate models in terms of estimates of conditional variances, estimates of conditional correlations and also in terms of computational complexity. 1

本研究用金融傳導的角度，從散裝海運產業切入，利用標普高盛商品指數、加權遠期運費協議指數、波羅的海運費指數、道瓊全球航運指數以及美元指數，以傳遞熵與BEKK-GARCH模型，探討2008年3月至2016年3月之散裝海運產業金融傳導因子，在多次金融危機中，散裝海運產業金融傳導因子的領先落後關係、短期報酬外溢效果與長期波動傳遞效果，以及對航運類股之影響。 本研究成果可從投資策略與經濟意涵兩方面呈現，在投資策略上，根據實證結果，在金融危機期間，資訊從道瓊全球航運指數流向波羅的海乾散貨運價指數，再流向加權遠期運費協議指數，代表股票市場領先運費市場，而運費市場又領先遠期運費協議市場，而每個期間的加權遠期運費協議指數對波羅的海乾散貨運價指數皆為正向顯著關係，波羅的海乾散貨運價指數與道瓊全球航運指數間皆為雙邊正向顯著關係，本研究建議預測波羅的海乾散貨運價指數的散裝海運產業業者與投資人，可以道瓊全球航運指數與加權遠期運費協議指數作為先行指標。 在經濟意涵方面，根據實證結果，金融危機期間，金融市場動盪程度提高，連帶影響散裝海運運價價格波動劇烈，使得散裝海運產業業者與投資人的避險需求提升，由於波羅的海乾散貨運價指數為散裝海運產業業者的每日報價，並非金融市場交易之結果，故散裝海運產業業者與投資人可以參考商品市場、股票市場、外匯市場及運費市場的資訊進行避險操作。

Cette thèse de doctorat a pour objectif principal d'étudier certaines propriétés probabilistes et statistiques de modèles de volatilité contenant des variables explicatives exogènes. Elle comporte deux parties.Dans une première partie, nous étudions le comportement asymptotique de l'estimation du quasi-maximum de vraisemblance (QMV) pour la classe polyvalente des modèles PGARCH semi-forts augmentés avec des covariables. Les hypothèses principales sur les variables exogènes sont la stationnarité et la non-colinéarité avec les autres variables explicatives de la volatilité. Pour la distribution asymptotique du QMV, nous étudions quatre situations différentes correspondant à des modèles forts ou semi-forts, et des paramètres à l'intérieur ou au bord de l'espace des paramètres. Nous montrons la normalité asymptotique du QMV sans imposer aucune condition de moment sur le processus observé lorsque le paramètre GARCH-X appartient à l'intérieur de l'espace des paramètres. Par contre, quand un ou plusieurs coefficients sont égaux à zéro, les conditions de moment d'ordre 4 sont requises pour que la matrice d'information soit finie et la loi asymptotique est alors la projection d'une loi normale sur un cône convexe . Comme la vraie valeur du paramètre n'est pas contrainte à appartenir à l'intérieur de l'espace des paramètres, nous proposons des tests pour déterminer l'ordre du modèle et vérifier la signification des variables exogènes. La deuxième partie est consacrée à l'étude de l'influence des variables exogènes sur les matrices de covariance conditionnelle de rendements d'actifs. Plus précisément, nous considérons des modèles BEKK avec variables exogènes. Les paramètres sont estimés par deux méthodes qui s'appellent l'estimation par ciblage de la variance et l'estimation équation par équation. Ces deux méthodes nous permettent de réduire la complexité numérique liée à l'estimation d'un nombre élevé des paramètre des modèles GARCH multivariés, en particulier, en présence de variables exogènes. La consistance ainsi que la loi limite de ces estimateurs sont établies pour des hypothèses relativement peu restrictives. En particulier, les innovations sont supposées être une différence de martingales au lieu d'être iid. Nos résultats sont illustrés par des expériences de Monte Carlo et des applications sur séries réelles. / This PhD Dissertation is dedicated to the study of probabilistic and statistical properties of volatility models augmented with exogenous variables. It consists of two parts which are summarized below. In the first part of this work, we study asymptotic behavior of the QMLE for the versatile class of the semi-strong PGARCH models augmented with exogenous variables. The main assumptions on the exogenous variables are the stationarity and the non-colinearity with the other explanatory variables of the volatility. For the asymptotic distribution of the QMLE, we investigated four different situations corresponding to strong or semi-strong models, and to parameters inside or at the boundary of the parameter space. When the GARCH-X parameter belongs to the interior of the parameter space, the asymptotic distribution of the QMLE is normal, whereas it is the projection of a normal distribution on a convex cone when one or several coefficients are equal to zero. For models with positive GARCH coefficients, the asymptotic distribution is obtained under very mild conditions, in particular, without any moment condition on the observed process. When the GARCH parameter stands at the boundary, fourth-order moment conditions are required for the information matrix to be finite. Our asymptotic results are obtained under conditions that are only marginally stronger than these optimal moment conditions, which extends and improves the results that existed for GARCH models without covariables. The second part is devoted to studying the influence of exogenous variables on the conditional covariance matrix of asset returns. Specifically, we consider BEKK models augmented with exogenous variables. The parameters are estimated by two methods which are called the variance targeting estimation and equation by equation estimation. Both methods allow us to reduce the curse of dimensionality which appears when modeling a conditional covariance matrix, particularly in the presence of exogenous variables. The consistency and the asymptotic distribution of these estimators are established under mild assumptions. In particular, the innovation is assumed to be a martingale difference instead of iid. Our results are illustrated by Monte Carlo experiences and the applications on real series.

Cette thèse de doctorat composée de trois chapitres contribue au développement de tests statistiques et à analyser la transmission financière dans un cadre multivarié hétéroscédastique. Le premier chapitre propose deux tests du multiplicateur de Lagrange de constance des corrélations conditionnelles dans les modèles GARCH multivariés. Si l'hypothèse nulle repose sur des corrélations conditionnelles constantes, l'hypothèse alternative propose une première spécification basée sur des réseaux de neurones artificiels et une seconde représentée par une forme fonctionnelle inconnue qui est linéarisée à l'aide d'un développement de Taylor.Dans le deuxième chapitre, un nouveau modèle est introduit dans le but de tester la non-linéarité des (co)variances conditionnelles. Si l'hypothèse nulle repose sur une fonction linéaire des innovations retardées au carré et des (co)variances conditionnelles, l'hypothèse alternative se caractérise quant à elle par une fonction de transition non-linéaire : exponentielle ou logistique ; une configuration avec effets de levier est également proposée. Dans les deux premiers chapitres, les expériences de simulations et les illustrations empiriques montrent les bonnes performances de nos tests de mauvaise spécification.Le dernier chapitre étudie la transmission d'information en séance et hors séance de cotation en termes de rendements et de volatilités entre la Chine, l'Amérique et l'Europe. Le problème d'asynchronicité est considéré avec soin dans la modélisation bivariée avec la Chine comme référence. / This Ph.D. thesis composed by three chapters contributes to the development of test statistics and to analyse financial transmission in a multivariate heteroskedastic framework.The first chapter proposes two Lagrange multiplier tests of constancy of conditional correlations in multivariate GARCH models. Whether the null hypothesis is based on constant conditional correlations, the alternative hypothesis proposes a first specification based on artificial neural networks, and a second specification based on an unknown functional form linearised by a Taylor expansion.In the second chapter, a new model is introduced in order to test for nonlinearity in conditional (co)variances. Whether the null hypothesis is based on a linear function of the lagged squared innovations and the conditional (co)variances, the alternative hypothesis is characterised by a nonlinear exponential or logistic transition function; a configuration with leverage effects is also proposed.In the two first chapters, simulation experiments and empirical illustrations show the good performances of our misspecification tests.The last chapter studies daytime and overnight information transmission in terms of returns and volatilities between China, America and Europe. The asynchronicity issue is carefully considered in the bivariate modelling with China as benchmark.