本研究探討VIX 期貨價格所隱含的資訊對於S&P 500 指數波動度預測的解釋力。過去許多文獻主要運用線性預測模型探討歷史波動度、隱含波動度和風險中立偏態對於波動度預測的資訊內涵。然而過去研究顯示，波動度具有長期記憶與非線性的特性，因此本文主要研究非線性預測模型對於波動度預測的有效性。本篇論文特別著重在不同市場狀態下(高波動與低波動)的實現波動度及隱含波動度異質自我迴歸模型(HAR-RV-IV model)。因此，本研究以考慮馬可夫狀態轉化下的異質自我迴歸模型(MRS-HAR model)進行實證分析。 本研究主要目的有以下三點: (1) 以VIX期貨價格所隱含的資訊提升S&P 500波動度預測的準確性。(2) 結合風險中立偏態與VIX期貨的資訊內涵，進一步提升S&P 500 波動度預測的準確性。(3) 考慮狀態轉換後的波動度預測模型是否優於過去文獻的線性迴歸模型。 本研究實證結果發現: (1) 相對於過去的實現波動度及隱含波動度，VIX 期貨可以提供對於預測未來波動度的額外資訊。 (2) 與其他模型比較，加入風險中立偏態和VIX 期貨萃取出的隱含波動度之波動度預測模型，只顯著提高預測未來一天波動度的準確性。 (3) 考慮狀態轉換後的波動度預測模型優於線性迴歸模型。 / This paper explores whether the information implied from VIX futures prices has incremental explanatory power for future volatility in the S&P 500 index. Most of prior studies adopt linear forecasting models to investigate the usefulness of historical volatility, implied volatility and risk-neutral skewness for volatility forecasting. However, previous literatures find out the long-memory and nonlinear property in volatility. Therefore, this study focuses on the nonlinear forecasting models to examine the effectiveness for volatility forecasting. In particular, we concentrate on Heterogeneous Autoregressive model of Realized Volatility and Implied Volatility (HAR-RV-IV) under different market conditions (i.e., high and low volatility state). This study has three main goals: First, to investigate whether the information extracted from VIX futures prices could improve the accuracy for future volatility forecasting. Second, combining the information content of risk-neutral skewness and VIX futures to enhance the predictive power for future volatility forecasting. Last, to explore whether the nonlinear models are superior to the linear models. This study finds that VIX futures prices contain additional information for future volatility, relative to past realized volatilities and implied volatility. Out-of-sample analysis confirms that VIX futures improves significantly the accuracy for future volatility forecasting. However, the improvement in the accuracy of volatility forecasts is significant only at daily forecast horizon after incorporating the information of risk-neutral skewness and VIX futures prices into the volatility forecasting model. Last, the volatility forecasting models are superior after taking the regime-switching into account.

This thesis in applied statistics and industrial economics examines the correlation between a number of market conditions on the Swedish and Global market and the yield difference between the Swedish stock market and the Global stock market. The report is based on data from the index MSCI Sweden Net Return, MSCI World Net Return and the Volatility index S&P 500. The market conditions that have been examined are Bull markets, Bear markets, periods of high volatility. We also examined how the appreciation of the SEK in comparison to the USD and the yield of the Swedish stock market correlated with the yield difference between the Swedish Stock Market and the Global stock market. The correlation was examined using multiple linear regression. The results indicated a positive correlation between the yield difference between the Swedish stock market and the Global stock market and the yield of the Swedish stock market, the appreciation of the SEK compared to the USD and Bull markets. We found a negative correlation with Bear markets and no correlation at all with the volatility.   The results are in line with what could be expected and give a stronger statistical ground for the idea that the Swedish stock market has larger fluctuations than the Global stock market during large-scale market fluctuations. / Detta kandidatexamensarbete inom tillämpad matematik och industriell ekonomi syftar till att undersöka hur avkastningsdifferensen mellan den Svenska och Globala aktiemarknaden korrelerar med ett antal olika marknadsförhållanden. Rapporten är baserad på data från MSCI Sweden Net Return och MSCI World Net Return samt Volatilitetsindex S&P500. De marknadsförhållanden som har undersökts är Bull markets, Bear markets, perioder då det råder hög volatilitet på marknaden. Vi undersökte även avkastningsdifferensens korrelation till kronans värdeförändring gentemot den Amerikanska dollarn och korrelationen till den Svenska aktiemarknadens värdeökning. Korrelationen undersöktes genom att utföra en multipel linjär regression. Resultaten visade på en rådande positiv korrelation mellan utvecklingen på den Svenska aktiemarknaden, prisutvecklingen av den Svenska kronan mot Amerikanska dollarn samt under Bull markets. Vi fann även en negativ korrelation med Bear markets och ingen korrelation till volatiliteten.   Resultaten är i linje med vad som kunde förväntas och ger en starkare statistisk grund till att den Svenska aktiemarknaden har större svängningar än den Globala aktiemarknaden vid stora marknadsfluktuationer.

The purpose of this study is to analyze if there is any tweet specific data posted by Donald Trump that has a correlation with the volatility of the stock market. If any details about the president Trump's tweets show correlation with the volatility, the goal is to find a subset of regressors with as high as possible predictability. The content of tweets is used as the base for regressors. The method which has been used is a multiple linear regression with tweet and volatility data ranging from 2010 until 2020. As a measure of volatility, the Cboe VIX has been used, and the regressors in the model have focused on the content of tweets posted by Trump using TF-IDF to evaluate the content of tweets. The results from the study imply that the chosen regressors display a small significant correlation of with an adjusted R2 = 0.4501 between Trump´s tweets and the market volatility. The findings Include 78 words with correlation to stock market volatility when part of President Trump's tweets. The stock market is a large and complex system of many unknowns, which aggravate the process of simplifying and quantifying data of only one source into a regression model with high predictability. / Syftet med denna studie är att analysera om det finns några specifika egenskaper i de tweets publicerade av Donald Trump som har en korrelation med volatiliteten på aktiemarknaden. Om egenskaper kring president Trumps tweets visar ett samband med volatiliteten är målet att hitta en delmängd av regressorer med för att beskriva sambandet med så hög signifikans som möjligt. Innehållet i tweets har varit i fokus använts som regressorer. Metoden som har använts är en multipel linjär regression med tweet och volatilitetsdata som sträcker sig från 2010 till 2020. Som ett mått på volatilitet har Cboe VIX använts, och regressorerna i modellen har fokuserat på innehållet i tweets där TF-IDF har använts för att transformera ord till numeriska värden. Resultaten från studien visar att de valda regressorerna uppvisar en liten men signifikant korrelation med en justerad R2 = 0,4501 mellan Trumps tweets och marknadens volatilitet. Resultaten inkluderar 78 ord som de när en är en del av president Trumps tweets visar en signifikant korrelation till volatiliteten på börsen. Börsen är ett stort och komplext system av många okända, som försvårar processen att förenkla och kvantifiera data från endast en källa till en regressionsmodell med hög förutsägbarhet.

In this thesis, we analyze premium relationship of American depositary receipts (ADR) and their underlying shares. Several researchers have previously identified the main variables influencing the construction of ADR premium of cross-listed companies. The aim of this study is to investigate to what extent the main variables affect differently the construction of ADR premium in crisis period. For the purpose of the study, two periods are defined. The period from June 2006 to October 2007 represents the non-crisis period whereas the period from October 2007 to March 2009 represents the crisis period. Our cross-listing sample consists of companies that have level II and level III ADR listed on the NYSE and the NASDAQ over the two periods. The tested variables influencing the premium are the liquidity, the currency exchange rate, the home and US market and the volatility. The liquidity is measured according to two ratios, the Amihud ratio and the turnover ratio. The currency exchange rate is the current exchange rate denominated in US dollar. The home markets are the reference indexes of the home country to which the underlying share of the ADR belong. The S&P 500 Index is used as a proxy for the US market. Finally, the US market volatility is analyzed with the CBOE VIX volatility Index. Multiple and simple OLS regressions are used to analyze the impacts of variables on ADR premium. The T-statistic is chosen to test the explanatory power of variables. The regressions are divided in three main parts. The first one is dedicated to the liquidity variables, then the second one to the home and US market, currency exchange rate and CBOE VIX volatility Index. Finally the last part keeps only the variables with the stronger explanatory power in order to define two equations of the factor influencing mostly the premium. We have found that crisis strongly modifies the relationship between ADR premium and the main variables. In crisis period, the regressions show that liquidity becomes a factor with a greater explanatory power of ADR premium. However the other main variables experience the opposite effect with a much lower T-test in times of crisis. It seems that the currency exchange rate, the home and US market as well as the volatility lose their explanatory power in times of crisis to the benefit of liquidity variables.

Η ακριβής πρόβλεψη της μελλοντικής μεταβλητότητας αποδεικνύεται ιδιαίτερα χρήσιμη για την τιμολόγηση παραγώγων προϊόντων και την αντιστάθμιση κινδύνων στη διαχείριση χαρτοφυλακίων. H τεκμαρτή μεταβλητότητα, όπως αυτή αντανακλάται στις τιμές των δικαιωμάτων προαίρεσης, αποτελεί την εκτίμηση της αγοράς για τη μελλοντική πραγματοποιηθείσα μεταβλητότητα και έχει αποδειχθεί ότι είναι πιο αποτελεσματική από την αντίστοιχη πρόβλεψη που προκύπτει από την ανάλυση ιστορικών χρονοσειρών. Η παρούσα διατριβή πραγματεύεται τη δημιουργία ενός δείκτη τεκμαρτής μεταβλητότητας για την Ελληνική χρηματιστηριακή αγορά, χρησιμοποιώντας έναν τρόπο υπολογισμού, ο οποίος είναι ανεξάρτητος από κάθε υπόδειγμα τιμολόγησης δικαιωμάτων προαίρεσης και βασίζεται σε ένα σταθμισμένο άθροισμα τιμών δικαιωμάτων. Η μεθοδολογία αυτή εφαρμόζεται για πρώτη φορά σε μια περιφερειακή, αναπτυσσόμενη αγορά, όπως το Χρηματιστήριο Αθηνών. Ο εν λόγω δείκτης τεκμαρτής μεταβλητότητας έχει τις προοπτικές να γίνει δείκτης αναφοράς των προσδοκιών για τη μελλοντική μεταβλητότητα στην Ελληνική μετοχική αγορά, καθώς αποδεικνύεται ότι υπερισχύει στατιστικά της ιστορικής μεταβλητότητας. Επίσης, οι επενδυτές του Χρηματιστηρίου Αθηνών μπορούν να χρησιμοποιούν το επίπεδό του και τις ημερήσιες μεταβολές του για να λάβουν επενδυτικές αποφάσεις, καθώς τα αποτελέσματα της οικονομετρικής ανάλυσης αποδεικνύουν ότι υπάρχει αρνητική και ασύμμετρη σχέση μεταξύ των μεταβολών του δείκτη τεκμαρτής μεταβλητότητας και των αποδόσεων του υποκείμενου μετοχικού δείκτη FTSE/Χ.Α.-20. Τέλος, η εμπειρική έρευνα καταγράφει την επιρροή της τεκμαρτής μεταβλητότητας των κυριοτέρων χρηματιστηρίων του εξωτερικού στην εγχώρια τεκμαρτή μεταβλητότητα, ενώ επιπλέον προσπαθεί να αναπτύξει ένα υπόδειγμα για την πρόβλεψη της τεκμαρτής μεταβλητότητας αυτής καθαυτής. / In this thesis a new measure of Greek stock market volatility based on the implied volatility of FTSE/ATHEX-20 index options is proposed. Greek Implied Volatility Index is calculated using the model-free methodology that involves option prices summations and is independent from the Black and Scholes pricing formula. The specific method is applied for the first time in a peripheral and illiquid market as the Athens Exchange. The empirical findings suggest that implied volatility includes information about future volatility beyond that contained in past realized volatility and in addition, prove that there is a statistically significant negative and asymmetric contemporaneous relationship between implied volatility changes and the underlying equity index returns. Finally, the volatility transmission effects on the Greek stock exchange from the major global exchanges are tested and documented. The basis of the international integration analysis, instead of the commonly used realized returns or variances, is the implied volatilities, as proxied by the corresponding implied volatility indices.

La première partie de cette thèse est consacrée aux problématiques liées à la modélisation markovienne de la courbe de variance forward. Elle est divisée en 3 chapitres. Dans le premier chapitre, nous présentons le cadre général de la modélisation de type HJM-Markov pour la courbe de variance forward. Nous revisitons le cadre affine-markovien modélisation et nous l'illustrons par l'exemple du modèle de Bühler. Dans le deuxième chapitre, nous proposons un nouveau modèle pour la courbe de variance forward qui combine les caractéristiques des deux versions (continue et discrète) du modèle de Bergomi 2008, sans se réduire ni à l'une ni à l'autre. Un des avantages de ce modèle est que les prix des futures et options sur VIX peuvent être exprimés comme des espérances de fonctions déterministes d'une variable aléatoire gaussienne, ce qui réduit le problème de la calibration à l'inversion de certaines fonctions monotones. Dans le troisième chapitre, on propose une méthode d'approximation pour les prix d'options européennes dans des modèles à volatilité stochastique de type multi-factoriels lognormal (comprenant le modèle présenté dans le deuxième chapitre, les modèles de Bergomi et le modèle de Scot 1987). Nous obtenons un développement d'ordre 3 de la densité du sous-jacent par rapport au paramètre de la volatilité de la volatilité. Nous présentons aussi une méthode de réduction de variance de type "variable de contrôle" pour la simulation par la méthode de Monte-Carlo qui utilise l'approximation explicite que nous obtenons de la fonction de répartition de la loi du sous-jacent. La deuxième partie de cette thèse est consacrée à l'étude des propriétés de monotonie des prix d'options européennes par rapport aux paramètres du CIR dans le modèle de Heston. Elle est divisée en deux chapitres. Dans le premier chapitre (cf. chapitre 4), nous donnons quelques résultats généraux sur le processus CIR. Nous montrons d'abord que les queues de distribution d'une combinaison du CIR et de sa moyenne arithmétique se comportent comme des exponentielles. Nous étudions ensuite les dérivées de la solution de ce processus par rapport aux paramètres de sa dynamique. Ces dérivées sont données comme solutions d'équations différentielles stochastiques, qu'on résout pour obtenir des représentations de ces dérivées en fonction des trajectoires du CIR. Le chapitre 5 est consacré à l'étude de la monotonie du prix d'un Put européen par rapport aux paramètres du CIR et à la corrélation dans le modèle de Heston. Nous montrons que, sous certaines conditions, les prix d'options européennes sont monotones par rapport aux paramètres du drift du CIR. Nous montrons ensuite que le paramètre de la volatilité de la volatilité joue le rôle de la volatilité si on prend la variance réalisée comme sous-jacent. En particulier, les prix d'options convexes sur la variance réalisée sont strictement croissants par rapport à la volatilité de la volatilité. Enfin, nous étudions la monotonie du prix du Put européen par rapport à la corrélation. Nous montrons que le prix du put du Put est croissant par rapport à la corrélation pour les petites valeurs du Spot et décroissant pour les grandes valeurs. Nous étudions ensuite les points de changement de monotonie pour les courtes et longues maturités

In this thesis, an analysis of Bitcoin, Monero price and volatility is conducted with respect to S&P500 and the VIX index. Moreover using Python, we computed correlation coefficients of nine cryptocurrencies with two different approaches: Pearson and Spearman from July 2016 -July 2018. Moreover the Pearson correlation coefficient was computed for each year from July2016 - July 2017 - July 2018. It has been concluded that in 2016 the correlation between the selected cryptocurrencies was very weak - almost none, but in 2017 the correlation increased and became moderate positive. In 2018, almost all of the cryptocurrencies were highly correlated. For example, from January until July of 2018, the Bitcoin - Monero correlation was 0.86 and Bitcoin - Ethereum was 0.82.

This thesis examines the effects of economic and political turbulence on coalition-formation across 37 EU and OECD democracies. Utilizing the existing potential-coalitions research, it analyzes how increases in turbulence affect common variables predicted to determine which coalitions are chosen of all potential cabinets following an election. These variables drawn from the coalition-formation field are examined using a conditional logit regression model with interaction effects, and results indicate that both political and economic turbulence highly affect the way coalition formation is carried out, although the effects of the two turbulence types vary. During economic turbulence larger coalitions appear to be warranted, although results simultaneously suggest that ideological cohesion is hard to achieve during turbulent times. During political turbulence, instead, results suggest ideologically wide coalitions are more common but that minority cabinets are still more likely to appear. Despite the varying results, this analysis finds support that coalition formation is greatly affected by both economic and political turbulence. While the effects of some coalition-formation variables utilized by previous researchers appear to withstand the addition of turbulence, other effects change greatly when levels of instability are considered.

本研究主要針對 Breidt et al.(1991) 等多位學者所建構的 Mixed causal-noncausal model,探討其假設與可拆解特性,並仔細討論相關資料模擬估計及預測的方法,最後將其實際應用於隱含波動率指數 (Volatility Index)的估計及預測上。根據本研究的實證結果,我們發現隱含波動率指數確實包含非因果的特性,並可進一步對其拆解及預測。另外 , 我們也以移動窗格的方式觀察係數估計結果的變化,發現 Mixed Causal-Noncausal Model 的確能夠捕捉到泡沫或危機正在生成的過程。 / This paper first focuses on Mixed causal-noncausal model constructed by Breidt et al.(1991) and then conducts empirical research on the CBOE Volatility Index. The assumptions, simulation, estimation and prediction methods of Mixed causal-noncausal model are introduced in great detail. Our empirical results show that the CBOE Volatility Index really contains non-causal parts, such that we can filter this part from the index and then further predict it. Moreover, by employing the rolling window estimation scheme the resulting coefficients of Mixed causal-noncausal model really could detect a bubble or a crisis which is going to happen.

This thesis performs portfolio optimization using three allocation methods, Certainty Equivalence Tangency (CET), Global Minimum Variance (GMV) and Minimum Conditional Value-at-Risk (MinCVaR). We estimate expected returns and covariance matrices based on 7 stock market indices with a DCC-GARCH model including an ARMA (1.1) process and an external regressor of an implied volatility index (VIX). We then simulate returns using a rolling window of 500 daily observations and construct portfolios based on the allocation methods. The results suggest that the model can sufficiently estimate expected returns and covariance matrices and we can outperform benchmarks in form of equally weighted and historical portfolios in terms of higher returns and lower risk. Over the whole out-of-sample period the CET portfolio yields the highest mean returns and GMV and MinCVaR can significantly lower the variance. The inclusion of VIX has marginal effects on the forecasting accuracy and it seems to impair the estimation of risk.