Cette thèse est consacrée à l'étude des applications de la théorie des erreurs par formes de Dirichlet. Notre travail se divise en trois parties. La première analyse les modèles gouvernés par une équation différentielle stochastique. Après un court chapitre technique, un modèle innovant pour les carnets d’ordres est proposé. Nous considérons que le spread bid-ask n'est pas un défaut, mais plutôt une propriété intrinsèque du marché. L'incertitude est portée par le mouvement Brownien qui conduit l'actif. Nous montrons que l'évolution des spread peut être évaluée grâce à des formules fermées et nous étudions l'impact de l'incertitude du sous-jacent sur les produits dérivés. En suite, nous introduisons le modèle PBS pour le pricing des options européennes. L'idée novatrice est de distinguer la volatilité du marché par rapport au paramètre utilisé par les traders pour se couvrir. Nous assumons la première constante, alors que le deuxième devient une estimation subjective et erronée de la première. Nous prouvons que ce modèle prévoit un spread bid-ask et un smile de volatilité. Les propriétés plus intéressantes de ce modèle sont l’existence de formules fermés pour le pricing, l'impact de la dérive du sous-jacent et une efficace stratégie de calibration. La seconde partie s'intéresse aux modèles décrit par une équation aux dérivées partielles. Les cas linéaire et non-linéaire sont analysés séparément. Dans le premier nous montrons des relations intéressantes entre la théorie des erreurs et celui des ondelettes. Dans le cas non-linéaire nous étudions la sensibilité des solutions à l’aide de la théorie des erreurs. Sauf dans le cas d’une solution exacte, il y a deux approches possibles : on peut d’abord discrétiser l’EDP et étudier la sensibilité du problème discrétisé, soit démontrer que les sensibilités théoriques vérifient des EDP. Les deux cas sont étudiés, et nous prouvons que les sharp et le biais sont solutions d’EDP linéaires dépendantes de la solution de l’EDP originaire et nous proposons des algorithmes pour évaluer numériquement les sensibilités. Enfin, la troisième partie est dédiée aux équations stochastiques aux dérivées partielles. Notre analyse se divise en deux chapitres. D’abord nous étudions la transmission de l’incertitude, présente dans la condition initiale, à la solution de l’EDPS. En suite, nous analysons l'impact d'une perturbation dans les termes fonctionnelles de l’EDPS et dans le coefficient de la fonction de Green associée. Dans le deux cas, nous prouvons que le sharp et le biais sont solutions de deux EDPS linéaires dépendantes de la solution de l’EDPS originaire / This thesis is devoted to the study of the applications of the error theory using Dirichlet forms. Our work is split into three parts. The first one deals with the models described by stochastic differential equations. After a short technical chapter, an innovative model for order books is proposed. We assume that the bid-ask spread is not an imperfection, but an intrinsic property of exchange markets instead. The uncertainty is carried by the Brownian motion guiding the asset. We find that spread evolutions can be evaluated using closed formulae and we estimate the impact of the underlying uncertainty on the related contingent claims. Afterwards, we deal with the PBS model, a new model to price European options. The seminal idea is to distinguish the market volatility with respect to the parameter used by traders for hedging. We assume the former constant, while the latter volatility being an erroneous subjective estimation of the former. We prove that this model anticipates a bid-ask spread and a smiled implied volatility curve. Major properties of this model are the existence of closed formulae for prices, the impact of the underlying drift and an efficient calibration strategy. The second part deals with the models described by partial differential equations. Linear and non-linear PDEs are examined separately. In the first case, we show some interesting relations between the error and wavelets theories. When non-linear PDEs are concerned, we study the sensitivity of the solution using error theory. Except when exact solution exists, two possible approaches are detailed: first, we analyze the sensitivity obtained by taking “derivatives” of the discrete governing equations. Then, we study the PDEs solved by the sensitivity of the theoretical solutions. In both cases, we show that sharp and bias solve linear PDE depending on the solution of the former PDE itself and we suggest algorithms to evaluate numerically the sensitivities. Finally, the third part is devoted to stochastic partial differential equations. Our analysis is split into two chapters. First, we study the transmission of an uncertainty, present on starting conditions, on the solution of SPDE. Then, we analyze the impact of a perturbation of the functional terms of SPDE and the coefficient of the related Green function. In both cases, we show that the sharp and bias verify linear SPDE depending on the solution of the former SPDE itself / Questa tesi é dedicata allo studio delle applicazioni della teoria degli errori tramite forme di Dirichlet, il nostro lavoro si divide in tre parti. Nella prima vengono studiati i modelli descritti da un’equazione differenziale stocastica: dopo un breve capitolo con risultati tecnici viene descritto un modello innovativo per i libri d’ordini. La presenza dei differenziali denarolettera viene considerata non come un’imperfezione, bensi una proprietà intrinseca dei mercati. L’incertezza viene descritta come un rumore sul moto Browniano sottostante all’azione; dimostriamo che l’evoluzione di questi differenziali puó essere valutata attraverso formule chiuse e stimiamo l’impatto dell’incertezza del sottostante sui prodotti derivati. In seguito proponiamo un nuovo modello, chiamato PBS, per il prezzaggio delle opzioni di tipo europeo: l’idea innovativa consiste nel distinguere la volatilità di mercato dal parametro usato dai trader per la copertura. Noi supponiamo la prima constante, mentre il secondo diventa una stima soggettiva ed erronea della prima. Dimostriamo che questo modello prevede dei differenziali lettera-denaro e uno smile di volatilità implicita. Le maggiori proprietà di questo modello sono l’esistenza di formule chiuse per il princing, l’impatto del drift del sottostante e un’efficace strategia per la calibrazione. La seconda parte è dedicata allo studio dei modelli descritti da delle equazioni alle derivate perziali. I casi lineare e non-lineare sono trattati separatamente. Nel primo caso mostriamo interessanti relazioni tra la teoria degli errori e quella delle wavelets. Nel caso delle EDP non-lineari studiamo la sensibilità della soluzione usando la teoria degli errori. Due possibili approcci esistono, salvo quando la soluzione è esplicita. Possiamo prima discretizzare il problema e studiare la sensibilità delle equazioni discretizzate, oppure possiamo dimostrare che le sensibilità teoriche verificano, a loro volta, delle EDP dipendenti dalla soluzione della EDP iniziale. Entrambi gli approcci sono descritti e vengono proposti degli algoritmi per valutare le sensibilità numericamente. Infine, la terza parte è dedicata ai modelli descritti da un’equazione stocastica alle derivate parziali. La nostra analisi é divisa in due capitoli. Nel primo viene studiato l’impatto di un’incertezza, presente nella condizione iniziale, sulla soluzione dell’EDPS, nella seconda si analizzano gli impatti di una perturbazione dei termini funzionali dell’EDPS del coefficiente della funzione di Green associata. In entrambi i casi dimostriamo che lo sharp e la discrepanza sono soluzioni di due EDPS lineari dipendenti dalla soluzione dell’EDPS iniziale

Submitted by Gustavo Silva Araujo (00araujogs@gmail.com) on 2013-12-11T15:36:37Z No. of bitstreams: 1 tese Gustavo Araujo.pdf: 1480340 bytes, checksum: 7f293b1022a44c6056c471633c80981d (MD5) / Approved for entry into archive by ÁUREA CORRÊA DA FONSECA CORRÊA DA FONSECA (aurea.fonseca@fgv.br) on 2013-12-16T12:31:03Z (GMT) No. of bitstreams: 1 tese Gustavo Araujo.pdf: 1480340 bytes, checksum: 7f293b1022a44c6056c471633c80981d (MD5) / Approved for entry into archive by Marcia Bacha (marcia.bacha@fgv.br) on 2013-12-19T16:32:32Z (GMT) No. of bitstreams: 1 tese Gustavo Araujo.pdf: 1480340 bytes, checksum: 7f293b1022a44c6056c471633c80981d (MD5) / Made available in DSpace on 2013-12-19T16:32:47Z (GMT). No. of bitstreams: 1 tese Gustavo Araujo.pdf: 1480340 bytes, checksum: 7f293b1022a44c6056c471633c80981d (MD5) Previous issue date: 2011-03-31 / This thesis is dedicated to studies in finance. The topics are distributed in two subareas, microstructure and asset pricing. There is also an insertion of the study in corporate finance, since we deal with the corporate governance of firms. In the first chapter I estimate the adverse selection cost component embedded in the spreads of Brazilian stocks. I also study the patterns of spreads and adverse selection costs as a function of the size and time of the trade. In chapter two, I implement an extensive research through a series of regressions in order to determine characteristics of the companies that are correlated with the adverse selection component and the spread. In particular, we analyze the relationship between the adverse selection and corporate governance levels. In the third chapter I detect which corporate governance mechanisms cause an opposite relationship between the returns of Brazilian stocks and corporate governance levels, as shown by Carvalhal and Nobili (2011). In this analysis, I emphasize the ownership concentration of Brazilian companies, which is extremely high when compared with more developed countries. / Esta tese se dedica a estudos na área de finanças. Os estudos se subdividem nas subáreas de microestrutura e apreçamento de ativos, mas há uma inserção do trabalho em finanças corporativas, uma vez que trato da governança corporativa das empresas. No primeiro capítulo estimo o coeficiente de assimetria de informação embutido no spread de compra e venda de ações brasileiras. Além disso, verifico se há padrões para esse coeficiente e para o próprio spread em relação ao tamanho da transação e à hora de negociação. No capítulo dois, eu investigo quais características ligadas às empresas têm relação com as variáveis estimadas no capítulo 1, o coeficiente de assimetria de informação embutido no spread de compra e venda de ações brasileiras e o próprio spread. A governança corporativa das empresas é uma das características examinadas. No terceiro capítulo, eu observo quais mecanismos de governança corporativa fazem com que haja uma relação antagônica entre os retornos das ações brasileiras e o índice de governança corporativa, conforme mostrado por Carvalhal e Nobili (2011). Nesta investigação, dou ênfase à concentração acionária das empresas brasileiras que, em comparação com países mais desenvolvidos, é extremamente alta.

Diese Dissertation zielt darauf ab, ein besseres Verständnis für Anomalien und Insiderhandel zu schaffen, sowie die Verfügbarkeit von qualitativ hochwertigen Daten für den deutschen Aktienmarkt zu verbessern. Der erste Aufsatz beinhaltet eine verzerrungsfreie Zeitreihe von monatlichen Renditen deutscher Aktien für die Jahre 1954 bis 2013, die auf der Basis stabiler Regeln berechnet und gut dokumentiert ist. Im Weiteren enthält der Aufsatz eine detaillierte Beschreibung des deutschen Aktienmarktes und dessen Besonderheiten, insbesondere im Vergleich zu den USA. Der zweite Aufsatz zeigt am Beispiel des Fama/French Drei-Faktoren-Modells die Probleme auf, die Anbieter und Nutzer von Faktorendaten haben, die sich nicht auf die USA beziehen. Die empirische Analyse von sieben Faktorensets für Deutschland zeigt, dass die Übernahme von Faktormodellen in einen anderen Kapitalmarkt eine komplexe Thematik ist. Der Aufsatz gibt Anregungen für Nutzer und Anbieter von Faktorensets und zeigt, wie die Wahl des Faktorensets das Ergebnis einer Studie beeinflussen kann. Im dritten Aufsatz werden verschiedene zyklische und antizyklische Handelsstrategien hinsichtlich ihrer Performance im deutschen Aktienmarkt untersucht. Von den untersuchten Strategien erscheint nur Momentum konsequent abnormale Renditen zu erzielen, dies auch nach Transaktionskosten. Die vierte Arbeit untersucht öffentlich bekannt gegebene Aktientransaktionen von Insidern börsennotierter deutscher Unternehmen. Der Aufsatz zeigt, dass Insider von TecDAX-Unternehmen und ihre Imitatoren hohe und statistisch signifikante abnormale Renditen erzielen. Insgesamt zeigt die Dissertation, dass methodische Variationen, die Verwendung verschiedener Untersuchungsdesigns, die Datenqualität und die Sorgfalt beim Erstellen von empirischen Analysen zur Beurteilung der Robustheit und der Stabilität der Ergebnisse unerlässlich sind. Der deutsche Aktienmarkt scheint effizienter zu sein als bisherigere Studien typischerweise nahelegen. / This doctoral thesis aims to contribute to a better understanding of stock market anomalies and insider trading as well as to improve the availability of high quality data for the German stock market. The first paper provides a sixty-year time series of monthly returns on German stocks that is constructed on the basis of stable rules, is well documented, includes all return components, and is free of biases. The paper also contains a detailed description of the German stock market, its peculiarities, regulation and differences as compared to the U.S. The second paper uses the Fama/French three-factor model as an example to point out the problems that providers and users of non-U.S factor data sets face. The empirical analysis of seven different factor data sets available for Germany shows that exporting a specific factor model from the U.S. to another capital market is neither an easy nor well-defined task. The paper gives suggestions to users and creators of factor sets and shows how the choice of a factor set affects the result of an empirical study. The third paper provides evidence on how various contrarian, momentum and seasonality strategies perform in the German stock market. Among these strategies, only momentum investing appears to earn persistently non-zero returns, even after transaction costs. The fourth paper studies publicly disclosed stock transactions by insiders of listed German firms. The paper finds that insiders of TecDAX firms earn large and statistically significant abnormal returns net of transaction costs; for DAX insiders they are indistinguishable from zero. Overall, this thesis illustrates that methodological variations, the use of different specifications, data quality and care when preparing empirical analyses is essential in the assessment of the robustness and stability of results. In sum, the German stock market appears to be more efficient than previous studies have typically suggested.

我國金融市場積極發展多元化與國際化，將由台灣期貨交易所推出臺指選擇權，建立選擇權市場以完備金融市場。由於選擇權市場掛牌交易契約眾多與選擇權的交易特性，因此有賴造市者發揮提供流動性、風險移轉、價格效率性及價格資訊揭露等經濟功能。本研究以造市者之功能性逐項比較我國造市者制度與EUREX、SEHK、LIFFE等各大交易所造市者制度之差異，用以發現我國首度引進的造市者制度對於選擇權市場發展的影響。 本研究為瞭解選擇權造市者營運的知識與技術，整理造市者作業循環的流程，針對造市者業務進行分工，建立起造市風險分析架構。推導得出造市風險包含造市交易風險與部位管理風險，呈現出市場波性風險、報價及交易策略風險、造市交易之市場機制風險、市場行情變動風險、遇險交易策略風險、部位管理之市場機制風險及財務與作業風險等七大類的造市風險。 本研究亦提出對於我國選擇權市場未來發展方向的關切，以及建議重視造市者利基與市場運作之關係，並提出未來與造市者相關之研究建議。 / Taiwan's financial market has been developing constructively into a globalization and multiplicity market within these years. To create a more completed financial market, Taiwan Futures Exchange (TAIFEX) will issue "the Taiwan stock index option" recently. As the complex and various features of the options trading, the option market will be successful and efficient through the market maker's economic functions, which are adding liquidity, increasing price efficiency, transferring risk and proving price information. This survey tried to compare the different functions of market maker system with TAIFEX, EUREX, SEHK and LEFFE, and to disclose the influence of the new market maker system on Taiwan's option market. This exposure takes great interest in market maker's knowledge and technology. By summarizing and classifying the operation process cycle flow of market maker, this research further organizes an analytic structure in market maker's risks. Including the market making risks and the positions management risks, the discussion demonstrates the market change risk, pricing strategy risk, limitary quoting risk, market volatility risk, hedging risk, mechanism risk, and finance and operation risk. The consequent also furnishes the concerns about the future development of Taiwan option market, emphasizing the importance of the relationship between market makers and market' benefit, and the suggestions to the further research.