Le développement des marchés électroniques organisés induit une pression constante sur la recherche académique en finance. L'impact sur le prix d'une transaction boursière portant sur une grande quantité d'actions sur une période courte est un sujet central. Contrôler et surveiller l'impact sur le prix est d'un grand intérêt pour les praticiens, sa modélisation est ainsi devenue un point central de la recherche quantitative de la finance. Historiquement, le calcul stochastique s'est progressivement imposé en finance, sous l'hypothèse implicite que les prix des actifs satisfont à des dynamiques diffusives. Mais ces hypothèses ne tiennent pas au niveau de la ``formation des prix'', c'est-à-dire lorsque l'on se place dans les échelles fines des participants de marché. Des nouvelles techniques mathématiques issues de la statistique des processus ponctuels s'imposent donc progressivement. Les observables (prix traité, prix milieu) apparaissent comme des événements se réalisant sur un réseau discret, le carnet d'ordre, et ceci à des échelles de temps très courtes (quelques dizaines de millisecondes). L'approche des prix vus comme des diffusions browniennes satisfaisant à des conditions d'équilibre devient plutôt une description macroscopique de phénomènes complexes issus de la formation des prix. Dans un premier chapitre, nous passons en revue les propriétés des marchés électroniques. Nous rappelons la limite des modèles diffusifs et introduisons les processus de Hawkes. En particulier, nous faisons un compte rendu de la recherche concernant le maket impact et nous présentons les avancées de cette thèse. Dans une seconde partie, nous introduisons un nouveau modèle d'impact à temps continu et espace discret en utilisant les processus de Hawkes. Nous montrons que ce modèle tient compte de la microstructure des marchés et est capable de reproduire des résultats empiriques récents comme la concavité de l'impact temporaire. Dans le troisième chapitre, nous étudions l'impact d'un grand volume d'action sur le processus de formation des prix à l'échelle journalière et à une plus grande échelle (plusieurs jours après l'exécution). Par ailleurs, nous utilisons notre modèle pour mettre en avant des nouveaux faits stylisés découverts dans notre base de données. Dans une quatrième partie, nous nous intéressons à une méthode non-paramétrique d'estimation pour un processus de Hawkes unidimensionnel. Cette méthode repose sur le lien entre la fonction d'auto-covariance et le noyau du processus de Hawkes. En particulier, nous étudions les performances de cet estimateur dans le sens de l'erreur quadratique sur les espaces de Sobolev et sur une certaine classe contenant des fonctions « très » lisses / The development of organized electronic markets induces a constant pressure on academic research in finance. A central issue is the market impact, i.e. the impact on the price of a transaction involving a large amount of shares over a short period of time. Monitoring and controlling the market impact is of great interest for practitioners; its modeling and has thus become a central point of quantitative finance research. Historically, stochastic calculus gradually imposed in finance, under the assumption that the price satisfies a diffusive dynamic. But this assumption is not appropriate at the level of ”price formation”, i.e. when looking at the fine scales of market participants, and new mathematical techniques are needed as the point processes. The price (last trade, mid-price) appears as events on a discrete network, the order book, at very short time scales (milliseconds). The Brownien motion becomes rather a macroscopic description of the complex price formation process. In the first chapter, we review the properties of electronic markets. We recall the limit of diffusive models and introduce the Hawkes processes. In particular, we make a review of the market impact research and present this thesis advanced. In the second part, we introduce a new model for market impact model at continuous time and living on a discrete space using process Hawkes. We show that this model that takes into account the market microstructure and it is able to reproduce recent empirical results as the concavity of the temporary impact. In the third chapter, we investigate the impact of large orders on the price formation process at intraday scale and at a larger scale (several days after the meta-order execution). Besides, we use our model to discuss stylized facts discovered in the database. In the fourth part, we focus on the non-parametric estimation for univariate Hawkes processes. Our method relies on the link between the auto-covariance function and the kernel process. In particular, we study the performance of the estimator in squared error loss over Sobolev spaces and over a certain class containing "very'' smooth functions

Ce travail de thèse aborde deux sujets : (i) L'utilisation d'une nouvelle méthode numérique pour l'évaluation des options sur un panier d'actifs, (ii) Le risque de liquidité, la modélisation du carnet d'ordres et la microstructure de marché. Premier thème : Un algorithme glouton et ses applications pour résoudre des équations aux dérivées partielles. L'exemple typique en finance est l'évaluation d'une option sur un panier d'actifs, laquelle peut être obtenue en résolvant l'EDP de Black-Scholes ayant comme dimension le nombre d'actifs considérés. Nous proposons d'étudier un algorithme qui a été proposé et étudié récemment dans [ACKM06, BLM09] pour résoudre des problèmes en grande dimension et essayer de contourner la malédiction de la dimension. L'idée est de représenter la solution comme une somme de produits tensoriels et de calculer itérativement les termes de cette somme en utilisant un algorithme glouton. La résolution des EDP en grande dimension est fortement liée à la représentation des fonctions en grande dimension. Dans le Chapitre 1, nous décrivons différentes approches pour représenter des fonctions en grande dimension et nous introduisons les problèmes en grande dimension en finance qui sont traités dans ce travail de thèse. La méthode sélectionnée dans ce manuscrit est une méthode d'approximation non-linéaire appelée Proper Generalized Decomposition (PGD). Le Chapitre 2 montre l'application de cette méthode pour l'approximation de la solution d'une EDP linéaire (le problème de Poisson) et pour l'approximation d'une fonction de carré intégrable par une somme des produits tensoriels. Un étude numérique de ce dernier problème est présenté dans le Chapitre 3. Le problème de Poisson et celui de l'approximation d'une fonction de carré intégrable serviront de base dans le Chapitre 4 pour résoudre l'équation de Black-Scholes en utilisant l'approche PGD. Dans des exemples numériques, nous avons obtenu des résultats jusqu'en dimension 10. Outre l'approximation de la solution de l'équation de Black-Scholes, nous proposons une méthode de réduction de variance des méthodes Monte Carlo classiques pour évaluer des options financières. Second thème : Risque de liquidité, modélisation du carnet d'ordres, microstructure de marché. Le risque de liquidité et la microstructure de marché sont devenus des sujets très importants dans les mathématiques financières. La dérégulation des marchés financiers et la compétition entre eux pour attirer plus d'investisseurs constituent une des raisons possibles. Dans ce travail, nous étudions comment utiliser cette information pour exécuter de façon optimale la vente ou l'achat des ordres. Les ordres peuvent seulement être placés dans une grille des prix. A chaque instant, le nombre d'ordres en attente d'achat (ou vente) pour chaque prix est enregistré. Dans [AFS10], Alfonsi, Fruth et Schied ont proposé un modèle simple du carnet d'ordres. Dans ce modèle, il est possible de trouver explicitement la stratégie optimale pour acheter (ou vendre) une quantité donnée d'actions avant une maturité. L'idée est de diviser l'ordre d'achat (ou de vente) dans d'autres ordres plus petits afin de trouver l'équilibre entre l'acquisition des nouveaux ordres et leur prix. Ce travail de thèse se concentre sur une extension du modèle du carnet d'ordres introduit par Alfonsi, Fruth et Schied. Ici, l'originalité est de permettre à la profondeur du carnet d'ordres de dépendre du temps, ce qui représente une nouvelle caractéristique du carnet d'ordres qui a été illustré par [JJ88, GM92, HH95, KW96]. Dans ce cadre, nous résolvons le problème de l'exécution optimale pour des stratégies discrètes et continues. Ceci nous donne, en particulier, des conditions suffisantes pour exclure les manipulations des prix au sens de Huberman et Stanzl [HS04] ou de Transaction-Triggered Price Manipulation (voir Alfonsi, Schied et Slynko) / This work is organized in two themes : (i) A novel numerical method to price options on manyassets, (ii) The liquidity risk, the limit order book modeling and the market microstructure.First theme : Greedy algorithms and applications for solving partial differential equations in high dimension Many problems of interest for various applications (material sciences, finance, etc) involve high-dimensional partial differential equations (PDEs). The typical example in finance is the pricing of a basket option, which can be obtained by solving the Black-Scholes PDE with dimension the number of underlying assets. We propose to investigate an algorithm which has been recently proposed and analyzed in [ACKM06, BLM09] to solve such problems and try to circumvent the curse of dimensionality. The idea is to represent the solution as a sum of tensor products and to compute iteratively the terms of this sum using a greedy algorithm. The resolution of high dimensional partial differential equations is highly related to the representation of high dimensional functions. In Chapter 1, we describe various linear approaches existing in literature to represent high dimensional functions and we introduce the high dimensional problems in finance that we will address in this work. The method studied in this manuscript is a non-linear approximation method called the Proper Generalized Decomposition. Chapter 2 shows the application of this method to approximate the so-lution of a linear PDE (the Poisson problem) and also to approximate a square integrable function by a sum of tensor products. A numerical study of this last problem is presented in Chapter 3. The Poisson problem and the approximation of a square integrable function will serve as basis in Chapter 4for solving the Black-Scholes equation using the PGD approach. In numerical experiments, we obtain results for up to 10 underlyings. Second theme : Liquidity risk, limit order book modeling and market microstructure. Liquidity risk and market microstructure have become in the past years an important topic in mathematical finance. One possible reason is the deregulation of markets and the competition between them to try to attract as many investors as possible. Thus, quotation rules are changing and, in general, more information is available. In particular, it is possible to know at each time the awaiting orders on some stocks and to have a record of all the past transactions. In this work we study how to use this information to optimally execute buy or sell orders, which is linked to the traders' behaviour that want to minimize their trading cost. In [AFS10], Alfonsi, Fruth and Schied have proposed a simple LOB model. In this model, it is possible to explicitly derive the optimal strategy for buying (or selling) a given amount of shares before a given deadline. Basically, one has to split the large buy (or sell) order into smaller ones in order to find the best trade-off between attracting new orders and the price of the orders. Here, we focus on an extension of the Limit Order Book (LOB) model with general shape introduced by Alfonsi, Fruth and Schied. The additional feature is a time-varying LOB depth that represents a new feature of the LOB highlighted in [JJ88, GM92, HH95, KW96]. We solve the optimal execution problem in this framework for both discrete and continuous time strategies. This gives in particular sufficient conditions to exclude Price Manipulations in the sense of Huberman and Stanzl [HS04] or Transaction-Triggered Price Manipulations (see Alfonsi, Schied and Slynko). The seconditions give interesting qualitative insights on how market makers may create price manipulations

This dissertation consists of five separate and self-contained essays. They have been written as distinct papers. Although there is a fair amount of overlap and cross-reference in analysis and discussion, the intention is that potential readers should be able to read them separately. Essay 1: An Empirical Analysis of the Trading Structure at the Stockholm Stock Exchange.This essay describes and analyzes the trading structure at the Stockholm Stock Exchange. In the empirical part, we report stylized facts based on intraday transaction and order book data, focusing on the intraday behavior of returns, trading activity, order placement and bid/ask spread, on the importance of the tick size and finally on some characteristics of the limit order book. Our main empirical conclusions are that a) the intraday U-shape in trading activity found in earlier U.S. studies on the whole also pertains to the Stockholm Stock Exchange, b) the limit order placement also follows an intraday U-shape, c) there is no distinct intraday pattern in returns, d) the volatility and bid/ask spread seems to be higher at the beginning of the trading day, e) the tick size is economically important, and f) the price impact of an order is a nonlinear function of its quantity, implying price inelastic demand and supply. Essay 2: An Empirical Analysis of the Trading Structure at the Stockholm Options and Forwards Exchange, OM.We first describe and analyze the trading structure at the Stockholm Options and Forward Exchange, OM Stockholm. It is characterized by some interesting market microstructure features, such as a high degree of transparency in a fully computerized trading system and a possibility to submit combination orders. We also present empirically results from tests on the intra- and interday trading volume of the OMX index derivatives, both in terms of number of contracts traded and in terms of number of transactions. There is evidence of a high degree of intraday variation in trading volume and some interday variation. The extension of trading hours of the underlying stocks, during the studied period should, according to modern trade concentration models, affect the distribution of trading across the day. Although no formal test of the models is possible with this data set, we are able to shed some supportive additional light on all of these models. Essay 3: Tick Size, Market Liquidity and Trading Volume: Evidence from the Stockholm Stock Exchange. (This essay was co-authored with Patrik Sandås.)The regulated tick size at a securities exchange puts a lower bound on the bid/ask spread. We use cross-sectional and cross-daily data from the Stockholm Stock Exchange to assess if this lower bound is economically important and if it has any direct effect on market depth and traded volume. We find a) strong support that the tick size is positively correlated to market depth and c) some support that it is negatively related to traded volume. We identify different groups of agents to whom a lower tick size would be beneficial and to whom it would be detrimental. Essay 4: An Analysis of the Lead-Lag Relationship between the OMX Index Forwards and the OMX Cash Index.This essay investigates the intraday lead-lag structure in returns between on the one hand the OMX cash index and on the other hand the OMX index forwards and the OMX synthetic index forwards in Sweden. The data set includes 22 months of data, from December 1991, to September 1993. It is divided into three sub-periods. The main conclusion is that there is a high degree of bidirectional interdependence, with both series Granger causing each other. Using a Sims-test, we find that the forwards as well as synthetic forwards lead the cash index with between fifteen and thirty minutes, while the cash index leads the forwards with about ten to fifteen minutes.. This implies a longer lead from the cash index to the forwards than in previous studies. The large interdependence could possibly be due to higher transaction costs, lower liquidity in the forward market and the specific trading environments used for Swedish securities. Essay 5: Order Flow Dynamics: Evidence from the Helsinki Stock Exchange. (This essay was co-authored with Kaj Hedvall.)This essay investigates the dynamics of the order flow in a limit order book. In contrast to previous studies, our data set from the Helsinki Stock Exchange encompasses the entire order book structure, including the dealer identities. This enables us to focus on the order behavior of individual dealers. We classify the events in the order book and study the structure of subsequent events using contingency tables. In specific, the structure of subsequent events initiated by the same dealer is compared to the overall event structure. We find that order splitting is more frequent than order imitation. Furthermore, if the spread increases as a result of a trade, other dealers quickly restore the spread, by submitting new limit orders. One conclusion is therefore that there exists a body of potential limit orders outside the formal limit order book and that there is a high degree of resiliency in our limit order book market. As a logical consequence, a large dealer strategically splits his order, in order for the market to supply additional liquidity. One interpretation of our results is that a limit order book market can accommodate larger orders than is first apparent by the outstanding limit orders. Another interpretation is that a limit order book structure gives room for informed traders to successively trade on their information. A third interpretation is that prices only slowly incorporate new information. / Diss. Stockholm : Handelshögskolan, 1994

During the last few years, market micro-structure research has been active in analysing the dependence of market efficiency on different market character­ istics. Make-take fees are one of those topics as they might modify the incen­ tives for participating agents, e.g. broker-dealers or market-makers. In this thesis, we propose a Hawkes process-based model that captures statistical differences arising from different fee regimes and we estimate the differences on limit order book data. We then use these estimates in an attempt to measure the execution quality from the perspective of a market-maker. We appropriate existing theoretical market frameworks, however, for the pur­ pose of hireling optimal market-making policies we apply a novel method of deep reinforcement learning. Our results suggest, firstly, that maker-taker exchanges provide better liquidity to the markets, and secondly, that deep reinforcement learning methods may be successfully applied to the domain of optimal market-making. JEL Classification Keywords Author's e-mail Supervisor's e-mail C32, C45, C61, C63 make-take fees, Hawkes process, limit order book, market-making, deep reinforcement learn­ ing kiselrastislavSgmail.com barunik@f sv.cuni.cz

Submitted by Guilherme Hideo Assaoka Hossaka (ghossaka@gmail.com) on 2018-09-07T17:43:58Z No. of bitstreams: 1 Stochastic_Supply_Curves_and_Liquidity_Costs.pdf: 6114705 bytes, checksum: 383773b2814d582892c750a566229869 (MD5) / Approved for entry into archive by Janete de Oliveira Feitosa (janete.feitosa@fgv.br) on 2018-09-18T13:52:02Z (GMT) No. of bitstreams: 1 Stochastic_Supply_Curves_and_Liquidity_Costs.pdf: 6114705 bytes, checksum: 383773b2814d582892c750a566229869 (MD5) / Made available in DSpace on 2018-09-26T20:00:18Z (GMT). No. of bitstreams: 1 Stochastic_Supply_Curves_and_Liquidity_Costs.pdf: 6114705 bytes, en checksum: 383773b2814d582892c750a566229869 (MD5) Previous issue date: 2018-06-26 / Market Liquidity is characterized by the easiness and freedom to trade assets at desired volumes and for prices perceived as representative of their values. When there is a scarcity of bid and ask offers at those terms, traders face the so called Market Liquidity Risk and they must offer concessions on their original offers, leading to additional costs. Approaches to model this phenomena exist in broad variety but a common component of most Market Liquidity models is an instantaneous cost component, also known as transaction/execution costs or realized/instantaneous impact. This element, here the Liquidity Cost, gives the actual trading prices faced by a trader, frequently a deviation from the unobservable “true price”, normally represented as a GBM with the mid-price as a proxy for modeling purposes. Although it is clear that Liquidity Costs are a relevant aspect of Market Liquidity Risk and it is present in many models, it is relegated to a more simplistic treatment, being though as well-behaved, deterministic, smooth and static. The main point of this work is to follow a different approach by evaluating Liquidity Costs at a microstructural level by estimating the Stochastic Supply Curve from C¸ etin-Jarrow-Protter Model for Brazilian equities. To do so, high-frequency-data from B3’s ftp is used and to build Limit Order Books for several stocks at intraday periods. The empirical findings support the existence of non-trivial Stochastic Supply Curves as a representation for Liquidity Costs in several equities on Brazilian Markets. Additionally, there is evidence that Liquidity Costs may behave in contrast with some of the literature, being stochastic with time-varying functional representations on the LOB and with liquidity parameters that could be represented as mean-reverting stochastic process.

This thesis consists of three related essays that examine investors' order submission strategies during the pre-opening period on the Malta Stock Exchange. The pre-opening is a period of liquidity formation and price discovery characterised by the absence of trade execution. The three essays collectively examine the information content of the order book in relation to: the intensity of order submissions, the aggressiveness of investors' order placement strategy and the determination of returns generated over the pre-opening period.The first essay empirically investigates if public information concerning the current state of the order book impacts the duration between order arrivals. Utilizing an augmented ACD model, the research reveals that the information which can be inferred from the characteristics of incoming orders has a more significant impact on the intensity of buy order submissions as compared to sell order submissions during the pre-opening period. Furthermore, prospective buyers appear to be more responsive to liquidity provided by the sell side than the reverse. Locked or crossed order submissions tend to increases (decreases) the intensity of order flow on the own (opposite) side of the order book, corroborating Cao et al. (2000) that such order-types contain informative signals about the fundamental value of the asset.The second essay analyses the impact of limit order book information on the aggressiveness observed in the submission, revision and cancellation of limit orders during the market pre-opening period. The empirical results indicate that the aggressiveness of order submissions and forward price revisions react both to the existing and subsequent changes in the execution probability at market opening, driven in part by the depth on either side of the order book. The aggressiveness of order cancellations increases on both sides of the order book when the depth at the top of the ask order book increases. In addition, the results suggest that the order book height and size of the inside spread impacts the aggressiveness of order submissions, revisions and cancellations.The third essay studies the contribution of the pre-opening period to the daily price discovery process and the factors that impact the return generated over this period. The results indicate that approximately one third of daily price discovery occurs in the pre-opening period. In addition, the impact of relative depth and height of the overnight and opening order book are concentrated at the top of the order book. Furthermore, cumulative changes to relative depth attributable to order submissions most significantly impact the opening returns of less actively traded stocks. The results show a strong relationship between opening returns and cumulative changes in the relative height along the order book attributable to order submissions, cancellations and forward and backward price revisions over the pre-opening period.

The object of master's thesis is to introduce to the financial derivatives and principals of trading on financial markets. We describe the methods used to search for arbitrage opportunities through statistical indicators and statistical characteristics, which are an integral part of the automatized trading systems. Analysis of the financial market is based on data derived from the interbank market.

The liquidity of financial assets can be studied in various different ways. In this thesis, liquidity is defined as the cost and time required to liquidate a position. While the liquidity of highly traded financial instruments like stocks is typically determined by analyzing the order book, the lack of an order book for over-the-counter bond trading presents challenges for estimating bond liquidity. The objective of this thesis is to develop a framework for estimating the cost and time required to liquidate a bond position. To achieve this, we propose a theoretical order book model based on the order book of more actively traded instruments, and estimate the model parameters using bond transaction data. The volume available to trade in the theoretical order book was modelled as gamma distributed stochastic process. The distribution of the liquidation cost could thereafter be derived where the parameters were estimated using the maximum likelihood estimation. The liquidation time, or liquidity horizon, was then determined through the solution of an optimization problem. The proposed framework for estimating bond liquidity produced promising results. The estimated parameters of the gamma distributed stochastic process accurately captured the behavior of bond trading volumes, allowing for a reliable estimation of the distribution of liquidation costs. Additionally, the optimization problem used to determine the liquidity horizon produced reasonable estimates. / Likviditeten hos finansiella tillgångar kan studeras på olika sätt. I denna uppsats definieras likviditeten som kostnaden och tiden som krävs för att likvidera en position. Medans likviditeten hos aktivt handlade finansiella tillgångar som aktier vanligtvis bestäms genom att analysera orderboken, så medför bristen på en orderbok för handel med "over-the-counter" obligationer utmaningar för att uppskatta likviditeten för dem. Syftet med denna uppsats är att utveckla ett ramverk för att uppskatta kostnaden och tiden som krävs för att likvidera en obligationsposition. För att uppnå detta föreslår vi en teoretisk orderboksmodell baserad på orderboken för mer aktivt handlade instrument, och uppskattar modellparametrarna med hjälp av data för obligationsaffärer. Volymen som är tillgänglig att handla i den teoretiska orderboken modellerades som en gammafördelad stokastisk process. Fördelningen av likvidationskostnaden kunde sedan härledas där parametrarna uppskattades med hjälp av maximum likelihood-estimering. Likvidationstiden, eller likvidationshoristonten, bestämdes sedan genom att lösa ett optimeringsproblem. Det föreslagna ramverket för att uppskatta likviditeten hos obligationer gav lovande resultat. De uppskattade parametrarna för den gammafördelade stokastiska processen fångade noggrant upp beteendet hos handelsvolymerna för obligationer, vilket möjliggjorde en pålitlig uppskattning av fördelning av likvidationskostnader. Optimeringsproblemet som användes för att bestämma likviditetshorisontens gav dessutom rimliga uppskattningar.

A stochastic model for the dynamics of a limit order book is evaluated and tested on empirical data. Arrival of limit, market and cancellation orders are described in terms of a Markovian queuing system with exponentially distributed occurrences. In this model, several key quantities can be analytically calculated, such as the distribution of times between price moves, price volatility and the probability of an upward price move, all conditional on the state of the order book. We show that the exponential distribution poorly fits the occurrences of order book events and further show that little resemblance exists between the analytical formulas in this model and the empirical data. The log-normal and Weibull distribution are suggested as replacements as they appear to fit the empirical data better.

Le contenu de cette thèse est divisé de la façon suivante. Après un premier chapitre d’introduction, le Chapitre 2 est consacré à introduire aussi simplement que possible certaines des théories qui seront utilisées dans les deux premiers articles. Dans un premier temps, nous discuterons des points importants pour la construction de l’intégrale stochastique par rapport aux semimartingales avec paramètre spatial. Ensuite, nous décrirons les principaux résultats de la théorie de l’évaluation en monde neutre au risque et, finalement, nous donnerons une brève description d’une méthode d’optimisation connue sous le nom de dualité. Les Chapitres 3 et 4 traitent de la modélisation de l’illiquidité et font l’objet de deux articles. Le premier propose un modèle en temps continu pour la structure et le comportement du carnet d’ordres limites. Le comportement du portefeuille d’un investisseur utilisant des ordres de marché est déduit et des conditions permettant d’éliminer les possibilités d’arbitrages sont données. Grâce à la formule d’Itô généralisée il est aussi possible d’écrire la valeur du portefeuille comme une équation différentielle stochastique. Un exemple complet de modèle de marché est présenté de même qu’une méthode de calibrage. Dans le deuxième article, écrit en collaboration avec Bruno Rémillard, nous proposons un modèle similaire mais cette fois-ci en temps discret. La question de tarification des produits dérivés est étudiée et des solutions pour le prix des options européennes de vente et d’achat sont données sous forme explicite. Des conditions spécifiques à ce modèle qui permettent d’éliminer l’arbitrage sont aussi données. Grâce à la méthode duale, nous montrons qu’il est aussi possible d’écrire le prix des options européennes comme un problème d’optimisation d’une espérance sur en ensemble de mesures de probabilité. Le Chapitre 5 contient le troisième article de la thèse et porte sur un sujet différent. Dans cet article, aussi écrit en collaboration avec Bruno Rémillard, nous proposons une méthode de prévision des séries temporelles basée sur les copules multivariées. Afin de mieux comprendre le gain en performance que donne cette méthode, nous étudions à l’aide d’expériences numériques l’effet de la force et la structure de dépendance sur les prévisions. Puisque les copules permettent d’isoler la structure de dépendance et les distributions marginales, nous étudions l’impact de différentes distributions marginales sur la performance des prévisions. Finalement, nous étudions aussi l’effet des erreurs d’estimation sur la performance des prévisions. Dans tous les cas, nous comparons la performance des prévisions en utilisant des prévisions provenant d’une série bivariée et d’une série univariée, ce qui permet d’illustrer l’avantage de cette méthode. Dans un intérêt plus pratique, nous présentons une application complète sur des données financières. / This thesis is structured as follows. After a first chapter of introduction, Chapter 2 exposes as simply as possible different notions that are going to be used in the two first papers. First, we discuss the main steps required to build stochastic integrals for semimartingales with space parameters. Secondly, we describe the main results of risk neutral evaluation theory and, finally, we give a short description of an optimization method known as duality. Chapters 3 and 4 consider the problem of modelling illiquidity, which is covered by two papers. The first one proposes a continuous time model for the structure and the dynamic of the limit order book. The dynamic of a portfolio for an investor using market orders is deduced and conditions to rule out arbitrage are given. With the help of Itô’s generalized formula, it is also possible to write the value of the portfolio as a stochastic differential equation. A complete example of market model along with a calibration method is also given. In the second paper, written in collaboration with Bruno Rémillard, we propose a similar model with discrete time trading. We study the problem of derivatives pricing and give explicit formulas for European option prices. Specific conditions to rule out arbitrage are also provided. Using the dual optimization method, we show that the price of European options can be written as the optimization of an expectation over a set of probability measures. Chapter 5 contained the third paper and studies a different topic. In this paper, also written with Bruno Rémillard, we propose a forecasting method for time series based on multivariate copulas. To provide a better understanding of the proposed method, with the help of numerical experiments, we study the effect of the strength and the structure of the different dependencies on predictions performance. Since copulas allow to isolate the dependence structure and marginal distributions, we study the impact of different marginal distributions on predictions performance. Finally, we also study the effect of estimation errors on the predictions. In all the cases, we compare the performance of predictions by using predictions based on a bivariate series and predictions based on a univariate series, which allows to illustrate the advantage of the proposed method. For practical matters, we provide a complete example of application on financial data.