由於一般投資人在買進或賣出選擇權時，並不會同時買進多個履約價的選擇權，故會造成選擇權隱含波動度的微笑曲線出現有不連續的現象。本文嘗試運用台指選擇權建構一個日內的隱含波動度微笑曲線交易策略，利用曲線配適的方法來捕捉瞬間時點下隱含波動度曲線發生不連續的現象，雖然最後出來的損益並不如預期但還是驗證了台指選擇權市場有多次這種不連續的機會且價格失衡的狀態會回歸正常。 / Option’s implied volatility smile curves discontinuous phenomenon exists when general investors buy or sell options, they won’t buy in every strike’s options. This paper attempts to use Taiwan Index Options (trading code: TXO) to construct a trading strategy based on the implied volatility. We use curve fitting method to capture volatility smile curve’s instant discontinuous. Although we find out that the strategy won’t make a profit, there were several times when TXO market’s implied volatility smile curves were discontinuous, and the market option price will eventually go back to the theoretical price.

Des travaux récents dans le domaine des mathématiques financières ont fait émerger l'importance de l'étude de la régularité et du comportement fin des queues de distribution pour certaines classes de diffusions à coefficients non globalement réguliers. Dans cette thèse, nous traitons des problèmes issus de ce contexte. Nous étudions d'abord l'existence, la régularité et l'asymptotique en espace de densités pour les solutions d'équations différentielles stochastiques en n'imposant que des conditions locales sur les coefficients de l'équation. Notre analyse se base sur les outils du calcul de Malliavin et sur des estimations pour les processus d'Ito confinés dans un tube autour d'une courbe déterministe. Nous obtenons des estimations significatives de la fonction de répartition et de la densité dans des classes de modèles comprenant des généralisations du CIR et du CEV et des modèles à volatilité locale-stochastique : dans ce deuxième cas, les estimations entraînent l'explosion des moments du sous-jacent et ont ainsi un impact sur le comportement asymptotique en strike de la volatilité implicite. La modélisation paramétrique de la surface de volatilité, à son tour, fait l'objet de la deuxième partie. Nous considérons le modèle SVI de J. Gatheral, en proposant une nouvelle stratégie de calibration quasi-explicite, dont nous illustrons les performances sur des données de marché. Ensuite, nous analysons la capacité du SVI à générer des approximations pour les smiles symétriques, en le généralisant à un modèle dépendant du temps. Nous en testons l'application à un modèle de Heston (sans et avec déplacement), en générant des approximations semi-fermées pour le smile de volatilité / Some recent works in the field of mathematical finance have brought new light on the importance of studying the regularity and the tail asymptotics of distributions for certain classes of diffusions with non-globally smooth coefficients. In this Ph.D. dissertation we deal with some issues in this framework. In a first part, we study the existence, smoothness and space asymptotics of densities for the solutions of stochastic differential equations assuming only local conditions on the coefficients of the equation. Our analysis is based on Malliavin calculus tools and on « tube estimates » for Ito processes, namely estimates for the probability that the trajectory of an Ito process remains close to a deterministic curve. We obtain significant estimates of densities and distribution functions in general classes of option pricing models, including generalisations of CIR and CEV processes and Local-Stochastic Volatility models. In the latter case, the estimates we derive have an impact on the moment explosion of the underlying price and, consequently, on the large-strike behaviour of the implied volatility. Parametric implied volatility modeling, in its turn, makes the object of the second part. In particular, we focus on J. Gatheral's SVI model, first proposing an effective quasi-explicit calibration procedure and displaying its performances on market data. Then, we analyse the capability of SVI to generate efficient approximations of symmetric smiles, building an explicit time-dependent parameterization. We provide and test the numerical application to the Heston model (without and with displacement), for which we generate semi-closed expressions of the smile

This diploma thesis is devoted to the linkages among stock, bond and foreign exchange markets in the Czech Republic, Austria, Germany and Poland during the period from the beginning of the year 2007 to the end of the year 2014. In order to complexly describe the interconnections among the markets, we utilized two kinds of spillover indices (from the generalized and structural VAR model), dynamic correlation coefficients obtained from the multivariate GARCH model and contemporaneous coefficients from the structural VAR model that was identified through heteroskedasticity in structural shocks. These methods enabled us to describe the linkages among the markets from different angles, to capture their time evolution and to obtain a notion about the transmission mechanism among these markets in Central Europe. The results, inter alia, indicate an intensifying interconnection among the markets during crisis periods, lowering impact of stock markets, increasing influence of bonds and a dominant role of German bonds and Austrian stocks. At the same time, we were able to capture the influence of the European sovereign debt crisis on the spillovers and on the intensity of linkages among the markets. We showed that the intensity of linkages among bond markets relented, probably as a result of higher emphasis on the...

This thesis investigates forecasting performance of Quantile Regression Neural Networks in forecasting multiperiod quantiles of realized volatility and quantiles of returns. It relies on model-free measures of realized variance and its components (realized variance, median realized variance, integrated variance, jump variation and positive and negative semivariances). The data used are S&P 500 futures and WTI Crude Oil futures contracts. Resulting models of returns and volatility have good absolute performance and relative performance in comparison to the linear quantile regression models. In the case of in- sample the models estimated by Quantile Regression Neural Networks provide better estimates than linear quantile regression models and in the case of out-of-sample they are equally good.

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 / The first part of this thesis deals with issues related to the Markov-modeling of the forward variance curve. It is divided into 3 chapters. In the first chapter, we present the general framework of the HJM-type modelling for the forward variance curve. We revisit the Affine-Markov framework, and illustrate by the model proposed by B"uhler 2006. In the second chapter, we propose a new model for the forward variance curve that combines features of the continuous and discrete version of Bergomi's model model Bergomi (2008), without being reduced to either of them. One of the strengths of this model is that the prices of VIX futures and options can be expressed as expectations of deterministic functions of a Gaussian random variable, which reduces the problem of calibration to the inversion of some monotonic functions. In the third chapter, we propose an approximation method for pricing of European options under some lognormal stochastic volatility models (including the model presented in the second chapter, Bergomi's model2008 and Scot model 1987). We obtain an expansion (with respect to the the volatility of volatility parameters of order 3) of the density of the underlying. We also propose a control variate method to effectively reduce variances of Monte Carlo simulations for pricing European optionsThe purpose of the second part of this thesis is to study the monotonicity properties of the prices of European options with respect to the CIR parameters under Heston model. It is divided into two chapters. In the first chapter (see Chapter 4), we give some general results related to the CIR process. We first show that the distribution tails of a combination of the CIR and its arithmetic mean behave as exponential. We then study the derivatives of the solution process with respect to the parameters of its dynamics. These data are derived as solutions of stochastic differential equations, which solves for the representations of these derivatives based on trajectories of the CIR. Chapter 5 is devoted to the study of the monotony of the European price of a put with respect to parameters of CIR and correlation in the Heston model. We show that under certain conditions, prices of European options are monotonic with respect to the parameters of the drift of the CIR. We then show that the parameter of the volatility of volatility plays the role of volatility if we take the realized variance as the underlying. In particular, prices of (convex) options on realized variance are strictly increasing with respect to the volatility of volatility. Finally, we study the monotony of the European Put prices with respect to the correlation. We show that the price of the put is increasing with respect to the correlation for small values ​​of Spot and decreasing for large values. We then study the change points of monotonicity for short and long maturities

Optimisation des modèles d'évaluation et de couverture d'options financières sous contraintes de liquidité / Optimization of pricing and hedging models for financial options under liquidity constraints

A presente pesquisa objetivou verificar se medidas contábeis calculadas por meio do lucro abrangente e de seus componentes são relevantes na explicação do risco das empresas. Para isso, analisou-se amostra composta por 105 companhias brasileiras de capital aberto com ações negociadas na BM&FBovespa. Foram selecionadas empresas não financeiras com dados disponíveis no período compreendido entre o primeiro trimestre de 2011 e o primeiro de trimestre de 2015, sendo excluídas empresas com ações de baixa liquidez. Inicialmente, avaliou-se por meio de análise de estatísticas descritivas e do Teste de Wilcoxon se o lucro abrangente é mais volátil que o lucro líquido. Esta primeira hipótese de pesquisa não foi refutada e se constatou que, para as empresas que compõem a amostra estudada, a volatilidade do lucro abrangente foi 30,84% superior à volatilidade do lucro líquido, evidenciando que a análise focada única e exclusivamente no lucro líquido induziria o usuário da informação contábil a ignorar possíveis fontes de risco da empresa. Para a análise da relevância do lucro abrangente e de seus componentes na explicação do risco, foi feita análise de regressão com dados em painel por meio de oito modelos estimados, cada qual com diferentes variáveis explicativas e abordagens de risco, estimado por meio da volatilidade dos retornos das ações (risco total) e do beta de mercado (risco sistemático). Os resultados apresentados evidenciaram que a relação entre a volatilidade do lucro abrangente e o risco da empresa é superior àquela observada entre a volatilidade do lucro líquido e o risco, porém tal relação não se mostrou estatisticamente significante. Todavia, verificou-se que a volatilidade do valor referente a outros resultados abrangentes possui relação negativa e estatisticamente significante com seu risco sistemático. Ganhos e perdas com hedges de fluxo de caixa e com ativos financeiros classificados como disponíveis para venda apresentaram relação negativa e estatisticamente significante com o risco da empresa, o que, de acordo com estudos anteriores, deve-se ao fato de que resultados não realizados estariam além do controle dos gestores. As evidências apresentadas pelo presente estudo corroboram a importância do assunto, fornecendo insumos para discussões sobre políticas contábeis relacionadas ao lucro e para o desenvolvimento de métricas contábeis para a avaliação do risco das empresas. / This research aimed to verify if the comprehensive income and its components are relevant in explanation of the firm risk. Thus, it analyzed sample of 105 Brazilian public companies listed on the BM&FBovespa. Non-financial companies with available data from the first quarter of 2011 to first quarter of 2015 were selected, being excluded companies with low stock liquidity. Initially, it was evaluated by analysis of descriptive statistics and the Wilcoxon test if the comprehensive income is more volatile than net income. This first research hypothesis was not refuted and found that for the companies in the sample, the volatility of comprehensive income was 30.84% higher than the volatility of net income, showing that an analysis focused exclusively on net income induce the accounting information user to ignore possible sources of firm risk. For the analysis of the relevance of comprehensive income and its components in risk explanation, regression analysis was done with panel data through eight estimated models, each with different explanatory variables and risk approaches, estimated by the volatility of stock returns (total risk) and market beta (systematic risk). The results showed that the relationship between the volatility of comprehensive income and the company\'s risk is greater than that observed between the volatility of net income and risk, but this relationship was not statistically significant. However, it was found that the volatility of the value related to other comprehensive income has negative and statistically significant relationship with its systematic risk. Gains and losses from cash flow hedges and financial assets classified as available for sale showed a negative and statistically significant relationship to the risk of the firm, which, according to previous studies, is due to the fact that unrealized results would be beyond the control of managers. The evidence presented in this study confirm the importance of the subject, providing inputs for discussions on accounting policies related to income and to the development of accounting metrics for risk assessment of companies.

This thesis focuses on analysis and comparison of volatility on selected European stock markets. At first paper briefly introduces the reader to the specific features of financial econometrics and the importance of asset returns volatility analysis. Further chapters precisely cover the construction of linear and nonlinear conditional heteroscedasticity models as an appropriate tool for describing the volatility in financial data. The empirical part of the thesis analyze four stock exchange indices from various European regions and seek appropriate models to express volatility behavior in period before the financial crisis in 2008 and also during the crisis phase. Based on selected models, the paper tries to compare the volatility in both periods within the specific stock market index and moreover between different regions. The last section examines asymmetric effects in volatility of stock indices using their graphical representation.

This diploma thesis describes problem of change-points in volatility of the time-series and their impact on price of nancial assets. Those change-points are estimated by using statistical methods and tests. Change-point estimation was tested on simulated datas and real world driven datas. Simulation helped to discover signi cant characteristics of change-point test, those data were simulated with using stochastic calculus. Google share prices and prices of call options were chosen to analyse impact of volatility change on those prices. Also implied volatility and its impact to call option price was analysed.

<p>We discuss the Normal inverse Gaussian (NIG) distribution in modeling volatility in the financial markets. Refining the work of Barndorff-Nielsen (1997) and Andersson (2001), we introduce a new parameterization of the NIG distribution to build the GARCH(p,q)-NIG model. This new parameterization allows the model to be a strong GARCH in the sense of Drost and Nijman (1993). It also allows us to standardized the observed returns to be i.i.d., so that we can use standard inference methods when we evaluate the fit of the model.</p><p>We use the realized volatility (RV), calculated from intraday data, to standardize the returns of the ECU/USD foreign exchange rate. We show that normality cannot be rejected for the RV-standardized returns, i.e., the Mixture-of-Distributions Hypothesis (MDH) of Clark (1973) holds. {We build a link between the conditional RV and the conditional variance. This link allows us to use the conditional RV as a proxy for the conditional variance. We give an empirical justification of the GARCH-NIG model using this approximation.</p><p>In addition, we introduce a new General GARCH(p,q)-NIG model. This model has as special cases the Threshold-GARCH(p,q)-NIG model to model the leverage effect, the Absolute Value GARCH(p,q)-NIG model, to model conditional standard deviation, and the Threshold Absolute Value GARCH(p,q)-NIG model to model asymmetry in the conditional standard deviation. The properties of the maximum likelihood estimates of the parameters of the models are investigated in a simulation study.</p>