Diese Arbeit enthält vier Aufsätze über die Beziehungen zwischen Handelsstrategien auf Aktienmärkten und dem Zustand des Marktes. Es werden ökonometrische Methoden angewendet um den Markteinfluss von limit order Platzierungen, die Eigenschaften von limit ordern sowie die Verwendung von versteckten ordern zu analysieren. Im Kapitel 1 quantifizieren wir die Effekte der limit order Platzierung auf Preisquotierungen am Börsenplatzes Euronext. Wir zeigen, dass eine limit order signifikante Informationen enthält und illustrieren inwieweit ihr Einfluss auf den Markt von ihren Charakteristika und dem Zustand des Orderbuchs abhängt. Das Kapitel 2 enthält empirische Resultate über die limit order Aktivität und den Markteinfluss von limit orders an der New Yorker NASDAQ Börse. Wir dokumentieren, dass Marktteilnehmer die Platzierung von limit orders mit kleinen Volumina präferieren, diese aber sofort nach ihrem Einsatz wieder löschen. Basierend auf der geschätzten Marktauswirkung einer limit order schlagen wir eine Methode zur Prognose ihres optimalen Volumens vor. Im Kapitel 3 werden die limit order-Strategien von Marktteilnehmern in intransparenten Märkten untersucht. Wir zeigen, dass die Position der sogenannten versteckten Liquidität im Orderbuch von diversen Variablen abhängt, die den Zustand des Marktes beschreiben. Die Daten suggerieren, dass Händler die Platzierung sogenannter hidden orders im Hinblick auf günstige Liquidität am Markt und dem "picking-off"-Risiko ausbalancieren. Im letzten Kapitel 4 präsentieren wir ein Softwaresystem zur Rekonstruktion von Orderbüchern und zur Extrahierung von Orderflussinformationen aus message stream Daten. Die Basismodule des Systems basieren auf allgemeinen Orderbuch-Ereignissen. Sie sind abstrakt gehalten und können so einfach auf beliebige Märkte mit elektronischen Orderbüchern angewendet werden. / In four essays, this thesis examines the interaction between traders'' strategies and the state of market by the econometric analysis of maket impact of limit order submission, the typical properties of order flow and the traders'' usage of hidden orders. Chapter 1 quantifies short-term and long-term effects of limit order submissions on quotes in Euronext. We show that limit orders have significant information content and the maginitude of their impact on the quotes depends on both the order''s characteritics and the state of limit order books (LOBs). Chapter 2 provides new empirical evidence on order submission activities and market impacts of limit orders at NASDAQ. We find that traders dominantly submit small size limit orders and cancell most of them immediately after submission. Based on the estimated market impact of orders, we propose a method to predict the optimal size of a limit order conditional on its position in the LOB and the desired impact. Chapter 3 analyzes traders'' decisions on using undisclosed orders in opaque markets. Our empirical findings show that market conditions affect traders'' order submission strategies and suggest that traders balance their hidden order placements to compete for the provision of liquidity and protect themselves against picking-off risk. Chapter 4 presents a program framework for reconstructing LOBs as well as extracting order flow information from message stream data. We design the basic modules of the system in an abstract layer based on common order events in limit order markets, so that it can be easily adapted to data at any limit order markets.

In dieser Dissertation befassen wir uns mit ökonometrischen Modellen und empirischen Eigenschaften von Intra-Tages (Hochfrequenz-) Aktienmarktdaten. Der Fokus liegt hierbei auf der Analyse des Einflusses, den die Veröffentlichung von Wirtschaftsnachrichten auf die Aktienmarktaktivität hat, der Vorhersage der Geld-Brief-Spanne sowie der Modellierung von Volatilitätsmaßen auf Intra-Tages-Zeitintervallen. Zunächst quantifizieren wir die Marktreaktionen auf Marktneuigkeiten innerhalb eines Handelstages. Zu diesem Zweck benutzen wir linguistisch vorab bearbeitete Unternehmensnachrichtendaten mit Indikatoren über die Relevanz, Neuheit und Richtung dieser Nachrichten. Mit einem VAR Modell für 20-Sekunden Marktdaten der London Stock Exchange weisen wir durch Nachrichten hervorgerufene Marktreaktionen in Aktienkursrenditen, Volatilität, Handelsvolumina und Geld-Brief-Spannen nach. In einer zweiten Analyse führen wir ein long memory autoregressive conditional Poisson (LMACP)-Modell zur Modellierung hoch-persistenter diskreter positivwertiger Zeitreihen ein. Das Modell verwenden wir zur Prognose von Geld-Brief-Spannen, einem zentralen Parameter im Aktienhandel. Wir diskutieren theoretische Eigenschaften des LMACP-Modells und evaluieren rollierende Prognosen von Geld-Brief-Spannen an den NYSE und NASDAQ Börsenplätzen. Wir zeigen, dass Poisson-Zeitreihenmodelle in diesem Kontext signifikant bessere Vorhersagen liefern als ARMA-, ARFIMA-, ACD- und FIACD-Modelle. Zuletzt widmen wir uns der optimalen Messung von Volatilität auf kleinen 20 Sekunden bis 5 Minuten Zeitintervallen. Neben der Verwendung von realized volatility-Ansätzen konstruieren wir Volatilitätsmaße durch Integration von spot volatility-Schätzern, sodass auch Beobachtungen außerhalb der kleinen Zeitintervalle in die Volatilitätsschätzungen eingehen. Ein Vergleich der Ansätze in einer Simulationsstudie zeigt, dass Volatilitätsmaße basierend auf spot volatility-Schätzern den RMSE minimieren. / In this thesis we present econometric models and empirical features of intra-daily (high frequency) stock market data. We focus on the measurement of news impacts on stock market activity, forecasts of bid-ask spreads and the modeling of volatility measures on intraday intervals. First, we quantify market reactions to an intraday stock-specific news flow. Using pre-processed data from an automated news analytics tool we analyze relevance, novelty and direction signals and indicators for company-specific news. Employing a high-frequency VAR model based on 20 second data of a cross-section of stocks traded at the London Stock Exchange we find distinct responses in returns, volatility, trading volumes and bid-ask spreads due to news arrivals. In a second analysis we introduce a long memory autoregressive conditional Poisson (LMACP) model to model highly persistent time series of counts. The model is applied to forecast quoted bid-ask spreads, a key parameter in stock trading operations. We discuss theoretical properties of LMACP models and evaluate rolling window forecasts of quoted bid-ask spreads for stocks traded at NYSE and NASDAQ. We show that Poisson time series models significantly outperform forecasts from ARMA, ARFIMA, ACD and FIACD models in this context. Finally, we address the problem of measuring volatility on small 20 second to 5 minute intra-daily intervals in an optimal way. In addition to the standard realized volatility approaches we construct volatility measures by integrating spot volatility estimates that include information on observations outside of the intra-daily intervals of interest. Comparing the alternative volatility measures in a simulation study we find that spot volatility-based measures minimize the RMSE in the case of small intervals.

Neste trabalho, apresentamos um conjunto de fatos empíricos e propriedades estatística de negociações em alta frequência, e discutimos algumas questões gerais comuns a dados de alta frequência tais: como discretização, espaçamento temporal irregular, durações correlacionadas, periodicidade diária, correlações temporais e as propriedades estatísticas dos fluxos de ordens. Logo apresentamos dois modelos da literatura,estilizados para a dinâmica do limit order book. No primeiro modelo os fluxo de ordens é descrito por processos de Poisson independentes, propomos para ele uma forma alternativa da prova de ergodicidade basejada em funções de Lyapunov. O segundo modelo é um modelo reduzido que toma em consideração dinâmicas tipo difusão para os tamanhos do bid e ask, e se foca só nas ordens como melhores preços, e modela explicitamente as cotações do bid e ask na presença de liquidez oculta. E por ultimo, propomos um modelo alternativo para a dinâmica do preço e do spread no limit order book, estudamos o comportamento assintótico do modelo e estabelecemos condições de ergodicidade e transitoridade. Além disso, consideramos a uma família de cadeias de Markov definidos nas sequências de caracteres (strings, ou palavras) com infinito alfabeto e para alguns exemplos inspirados nos modelos de negociações em alta frequência, obtemos condições para ergodicidade, transitoriedade e recorrência nula, para a qual usamos as técnicas de construção de funções Lyapunov. / In this work, we present a set of empirical facts and statistical properties of negotiations at high frequency and discuss some general issues common to high-frequency data such: as discretization, irregular spacing, correlated durations, daily periodicity, temporal correlations and the statistical properties of flows orders. Soon we present two models stylized in the literature for the dynamic limit order book. In the first model the order flow described by separate Poisson processes and we propose it to an alternative form of test ergodicity based on Lyapunov function. The second model is a reduced model that takes into consideration diffusion-type dynamics for the sizes of the bid and ask, and focus only on orders as best price and model explicitly quotes the bid and ask in the presence of hidden liquidity. And finally, we propose an alternative model for the price dynamics and spread in the limit order book, we study the asymptotic behavior of the model and established conditions of ergodicity. Furthermore, we consider the a family of Markov chains defined on the sequences of characters (strings, or words) with infinite alphabet. For some examples inspired by the models of high frequency trading we obtain a conditions for ergodicity, transience and null-recurrence. In order to prove this we use the construction of Lyapunov functions techniques.

本篇論文基於市場上所存在的一些交易機制，探討漲跌停前後之股價行為。因為證券市場上存在一些交易規則，例如漲跌停限制、買賣價差、最小升降單位限制、競價制度等，這些交易規則，具有法定的效力，理所當然地會影響投資人的行為。這種以各種交易機制的存在，探討價格形成的過程，就是市場微結構理論之研究範疇。 本篇引用Hausman, Lo, and MacKinlay (1992)所建立之Ordered Probit模型來分析漲跌停前後之股價行為，以個股逐筆交易的價格變動為因變數，而建立因變數為間斷型之分析模型，並以等待撮合時間、交易量、落後期交易價格、買賣價差等經濟變數，來探討個股逐筆交易價格變動的成因。在此同時，鑑於以往研究多假定價量關係為線性，本研究引入非線性的概念，檢定價量之間是否存有非線線性之關係；最後，為使模型更具解釋力，我們引入異質性變異數。 第一章 緒論……………………………………………………………..1 第一節 研究動機……………………………………………..1 第二節 研究目的……………………………………………..7 第三節 研究範圍與限制……………………………………..7 第四節 研究架構與內容……………………………………..8 第二章 文獻回顧……………………………………………………….10 第一節 非同時交易………………………………………….10 第二節 最小升降單位……………………………………….11 第三節 買賣價差…………………………………………….14 第四節 漲跌停限制………………………………………….15 第五節 重要模型回顧…………………………………….…18 2.5.1 Chou(1996)……………………………………..18 2.5.2 Hausman, Lo, and MacKinlay(1992)…………..20 第三章 實證模型設定………………………………………………….25 第一節 資料來源…………………………………………….25 第二節 樣本選取…………………………………………….25 第三節 模型設定…………………………………………….26 3.3.1 價格的變動區間……………………………….26 3.3.2 解釋變數……………………………………….29 3.3.3 條件變異數的型式…………………………….32 3.3.4 價格與成交量之間非線性關係的檢定……….32 第四節 資料處理…………………………………………….33 第四章 實證分析……………………………………………………….36 第一節 模型基本統計分析………………………………….36 第二節 價量非線性關係的檢定…………………………….39 第三節 Ordered Probit模型實證分析……………………….40 第五章 結論與建議……………………………………………………..48 第一節 結論…………………………………………………..48 第二節 建議…………………………………………………..49 參考文獻…………………………………………………………………..50 / This thesis is an application of the market microstructure theory’. In light of some trading mechanisms in our stock market, such as price limit, bid-asked spread, tick size, and auction system, those trading rules would influence the behavior of investors. We want to study the process and outcomes of stock price under those explicit trading rules. We use the Ordered Probit model (Hausman, Lo, and MacKinlay, 1992) to investigate the stock behaviors when it hits price limits. We also use price change as the discrete dependent variable, and time elapsed, trading volume, lag price changes, bid-asked spread as explanatory variables. In order to make the model more explainable, heterogeneity is applied. Moreover, we also want to find out if there is any nonlinear relationship between price change and trading volume.

<p>The work is focused on the Value at Risk and the Expected Shortfallcalculation. We assume the returns to be based on two pillars - the white noise and the stochastic volatility. We assume that the white noise follows the NIG distribution and the volatility is modeled using the nGARCH, NIG-GARCH, tGARCH and the non-parametric method. We apply the models into the stocks of three Banks of the Nordic market. We consider the daily and the intraday returns with the frequencies 5, 10, 20 and 30 minutes. We calculate the one step ahead VaR and ES for the daily and the intraday data. We use the Kupiec test and the Markov test to assess the correctness of the models. We also provide a new concept of improving the daily VaR calculation by using the high frequency returns. The results show that the intraday data can be used to the one step ahead VaR and the ES calculation. The comparison of the VaR for the end of the following trading day calculated on the basis of the daily returns and the one computed using the high frequency returns shows that using the intraday data can improve the VaR outcomes.</p>

The work is focused on the Value at Risk and the Expected Shortfallcalculation. We assume the returns to be based on two pillars - the white noise and the stochastic volatility. We assume that the white noise follows the NIG distribution and the volatility is modeled using the nGARCH, NIG-GARCH, tGARCH and the non-parametric method. We apply the models into the stocks of three Banks of the Nordic market. We consider the daily and the intraday returns with the frequencies 5, 10, 20 and 30 minutes. We calculate the one step ahead VaR and ES for the daily and the intraday data. We use the Kupiec test and the Markov test to assess the correctness of the models. We also provide a new concept of improving the daily VaR calculation by using the high frequency returns. The results show that the intraday data can be used to the one step ahead VaR and the ES calculation. The comparison of the VaR for the end of the following trading day calculated on the basis of the daily returns and the one computed using the high frequency returns shows that using the intraday data can improve the VaR outcomes.

Aquesta tesi ofereix un examen en profunditat del comportament d’apreuament de les accions dipositades per part dels mercats emergents que, en gran part, s’han menystingut tot i el seu paper de dominació en l’àmbit del creuament de cotitzacions estrangeres. Les característiques de les accions dipositades fan que tinguin un valor idèntic al del seu stock subjacent i, per tant, esperen ser valorades de la mateixa manera. El fet de dur a terme una anàlisi detallada d’aquesta qüestió ha estat obstaculitzat fins ara per la falta de qualitat de les dades del dia a dia dels mercats emergents, unes informacions que faciliten l’anàlisi a temps real de la relació entre els preus de les accions dipositades i els seus stocks subjacents. Aquest estudi directe és necessari des del moment que aquests mercats tenen grans barreres comercials que possiblement distorsionen les relacions d’apreuament teòriques i emmascaren els veritables patrons d’apreuament. En el primer assaig s’examina el llarg funcionament fonamental de la relació econòmica que lliga els dos valors: la llei del preu únic. Proves recents demostren que, contràriament a allò que ocorre amb els valors de mercat, l’equitat de preus es trenca en els valors dels mercats emergents a causa de la presència de barreres comercials com ara els preus de comerç, les restriccions de la venda al detall i el control de capital. En el primer assaig es confirma la violació de la llarga carrera de la paritat en els preus de les accions dipositades egípcies, fet que està corroborat per proves de fortalesa dutes a terme durant diversos caps de setmana al mercat local i al mercat amfitrió, com també en els moviments del règim del tipus de canvi. El segon assaig se centra a identificar si existeixen oportunitats reals d’arbitratge quan es viola l’equilibri en la relació d’apreuaments subjacent. En l’anàlisi s’utilitza una única freqüència elevada durant dos anys de dades diàries de 16 valors egipcis i argentins per identificar si existeixen oportunitats d’arbitratge durant el període en què els dos valors estan comerciant i establir si les comercialitzacions d’arbitratge juguen algun paper en la convergència de preus. La metodologia emprada es basa en un procediment d’identificació del nou arbitratge que té en compte les despeses del comerç dinàmic i el volum d’aquest. S’ha establert una evidència de la presència d’un gran nombre d’oportunitats d’arbitratge a través de la mostra. S’ha vist que les oportunitats d’arbitratge persisteixen durant uns quants minuts i demanen més d’una comercialització per convergir en zones no arbitrades. A partir d’un algoritme de filtració s’extreuen les veritables comercialitzacions d’arbitratge de la comercialització d’arbitratge de les dades i s’estableix la importància del rol d’arbitratge en el moment de restablir els preus al seu valor fonamental i en el moment d’evitar que els preus vagin a la deriva lluny d’un preu implícit comú i eficient. El tercer assaig afegeix l’anàlisi de l’arbitratge i fa servir les mateixes dades diàries per examinar si és el mercat local o l’estranger el que juga un paper més dominant en l’apreuament diari dels valors de les cotitzacions creuades egípcies i argentines. Els resultats mostren que els dos mercats són importants per al procés de descobriment de preus, però que tant per a tots els valors egipcis com per a la major part dels argentins, el mercat local juga un paper més dominant. S’ha determinat que la localització de la descoberta del preu depèn de múltiples factors, entre els quals la liquiditat i el volum de comercialitzacions que cada mercat pot atraure són els més importants. El darrer assaig de la tesi va estar motivat pels resultats del tercer assaig i inspirat pels moviments de la Primavera Àrab de l’Orient Mitjà. L’aixecament a Egipte del 25 de gener va estar acompanyat pel tancament complet dels mercats d’stock durant dos mesos sencers. Aquest fet va crear una situació interessant en la qual els únics valors egipcis que podien comercialitzar eren aquells que tenien accions dipositades i que comercialitzaven al Regne Unit. Utilitzem aquest fet per examinar l’efecte d’un canvi en el marc legal en la localització de la descoberta del preu i per determinar que durant el període d’excepció durant el qual el mercat local va estar tancat, la localització de la descoberta del preu va canviar al mercat estranger, fent que aquest fos la localització dominant per a les activitats d’apreuament. Això proporciona dades de la naturalesa dinàmica del descobriment de preus de les accions dipositades. / Esta tesis ofrece un examen en profundidad del comportamiento de pricing de los recibos de depósito por parte de los mercados emergentes que, en gran parte, ha sido negligido a pesar de su papel dominante en el ámbito del cross-listing extranjero. Las características de los recibos de depósito hacen que sean títulos idénticos a su stock subyacente y, por tanto, se espera que sean valorados de la misma forma. El análisis detallado esta cuestión ha visto obstaculizado hasta ahora por la falta de datos de calidad intradía de los mercados emergentes, que facilite el análisis en tiempo real de la relación entre los precios de los recibos de depósito y su stock subyacente. Este análisis directo es necesario desde el momento que estos mercados tienen grandes barreras comerciales que posiblemente distorsionan las relaciones de pricing teóricas y enmascaran los verdaderos patrones de pricing. En el primer estudio, se examina la relación económica fundamental a largo plazo que relaciona los dos títulos: la ley del precio único. Pruebas recientes demuestran que, contrariamente a aquello que ocurre con los valores del mercado desarrollado, la paridad de precios se rompe en los valores de los mercados emergentes debido a la presencia de barreras comerciales como los precios comerciales, las restricciones de venta a corto y el control de capital. Este primer estudio confirma la violación de la paridad de precios de los recibos de depósito egipcios, hecho que está corroborado por los tests de fortaleza llevados a cabo durante varios fines de semana entre el mercado local y el de acogida, como también en los cambios de régimen del tipo de cambio. El segundo estudio se centra en identificar si existen oportunidades reales de arbitraje cuando se viola la relación de pricing de equilibrio subyacente. En el análisis, se usa una única serie de datos intradía de alta frecuencia durante dos años de 16 valores egipcios y argentinos para identificar si existen oportunidades de arbitraje durante el período en que los dos valores se están comerciando y establecer si las comercializaciones de arbitraje tienen algún papel en la convergencia de precios. La metodología usada se basa en un nuevo procedimiento de identificación del arbitraje que tiene en cuenta los costes comerciales dinámicos y los volúmenes. Se ha constatado que existe un gran número de oportunidades de arbitraje a lo largo de la muestra. Se ha visto que las oportunidades de arbitraje persisten durante unos cuantos minutos y requieren más de una comercialización para converger en zonas no arbitradas. A partir de un algoritmo de filtración, se extraen los intercambios reales de arbitraje de los intercambios de la serie de datos y se establece la importancia del rol de los árbitros para restablecer los precios a sus valores fundamentales y evitar que los precios se alejen de un precio implícito común y eficiente. El tercer estudio se basa en el análisis del arbitraje y utiliza la misma serie de datos intradía para examinar si es el mercado local o el extranjero el que tiene un papel más dominante en el pricing intradía de los valores de las cotizaciones cruzadas egipcias y argentinas. Los resultados muestran que los dos mercados son importantes para el proceso de revelación del precio, pero que para todos los valores egipcios y para la mayor parte de los argentinos el mercado local tiene un papel más dominante. Se ha observado que la localización de la revelación del precio depende de múltiples factores, entre los cuales la liquidez y el volumen de comercialización que cada mercado puede atraer son los más importantes. El último estudio de esta tesis fue motivado por los resultados del tercer estudio e inspirado por los movimientos de la Primavera Árabe del Oriente Medio. La revuelta del 25 de enero vino acompañado por el cierre total de los mercados bursátiles durante dos meses enteros. Este hecho creó un escenario interesante en el cual los únicos valores egipcios que se podían comercializar eran aquellos que tenían recibos de depósito y que comercializaban en el Reino Unido. Utilizamos este hecho para examinar el efecto de un cambio en el marco legal de la locación del descubrimiento del precio y para ver que durante el período de excepción durante el cual el mercado estuvo cerrado, la localización de la revelación del precio ha pasado al mercado emergente, haciendo que este fuera la localización dominante para las actividades de pricing. Esto demuestra la naturaleza dinámica del descubrimiento de precios de los recibos de depósito. / This thesis provides an in-depth examination of the pricing behavior of depository receipts from emerging markets which have been largely overlooked despite their dominating role in the foreign cross-listing arena. Characteristics of depository receipts make them identical securities to their underlying stock and therefore both are expected to be priced equally. A detailed analysis of the issue has been so far hampered by the lack of quality intraday data from emerging markets that facilitates a real time analysis of the relationship between the prices of the depository receipt and its underlying stock. This direct examination is required since those markets have large trading barriers that are hypothesized to distort the theoretical pricing relationship and mask true pricing patterns. The first essay examines the fundamental long run economic relationship that ties both securities: the law of one price. Recent evidence shows that contrary to developed market equities, price parity is broken in emerging market equities due to the presence of trading barriers such as trading costs, short selling restrictions and capital controls. The first essay confirms the violation of long run price parity in Egyptian depository receipts which is corroborated by robustness tests around the different weekends between the local and host market as well as around exchange rate regime shifts. The second essay focuses on identifying whether real arbitrage opportunities exist when the underlying equilibrium pricing relationship is violated. The analysis uses a unique two year high frequency intraday dataset from 16 Egyptian and Argentinean equities to identify whether arbitrage opportunities exist during the period when both securities are simultaneously trading and establish whether arbitrage trades play a role in price convergence. The methodology used relies on a novel arbitrage identification procedure that uses dynamic trading costs and volumes. Evidence of the presence of large number of arbitrage opportunities across the sample is established. Arbitrage opportunities are found to persist for several minutes and require more than one trade to converge to no-arbitrage zones. A filtering algorithm extracts real arbitrage trades from the arbitrage trades from the dataset and establishes the important role of arbitrageurs in restoring prices to their fundamental values and in keeping prices from drifting away from a common efficient implicit price. The third essay builds on the arbitrage analysis and uses the same intraday dataset to examine whether the local or foreign market plays a more dominant role in the intraday pricing of the Egyptian and Argentinean cross-listed securities. The results show that both markets are important for the price discovery process, but that for all of the Egyptian and most of the Argentinean securities, the local market plays a more dominant role. The location of price discovery is found to depend on several factors, most importantly the liquidity and trading volume that each market can attract. The final essay in the thesis was motivated by the results of the third essay and inspired by the Arab spring movements in the Middle East. The 25th of January uprising in Egypt was accompanied by a full stock market closure for a complete two months. This created an interesting setting in which the only Egyptian equities that were allowed to trade were those with depository receipts trading in the UK. We use this event to examine the effect of a change in the legal environment on the location of price discovery and find that during the interim period where the local market was closed, the location of price discovery has shifted to the foreign market making it the dominant location for pricing activity. This provides evidence of the dynamic nature of the price discovery of depository receipts.

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Neste trabalho, apresentamos um conjunto de fatos empíricos e propriedades estatística de negociações em alta frequência, e discutimos algumas questões gerais comuns a dados de alta frequência tais: como discretização, espaçamento temporal irregular, durações correlacionadas, periodicidade diária, correlações temporais e as propriedades estatísticas dos fluxos de ordens. Logo apresentamos dois modelos da literatura,estilizados para a dinâmica do limit order book. No primeiro modelo os fluxo de ordens é descrito por processos de Poisson independentes, propomos para ele uma forma alternativa da prova de ergodicidade basejada em funções de Lyapunov. O segundo modelo é um modelo reduzido que toma em consideração dinâmicas tipo difusão para os tamanhos do bid e ask, e se foca só nas ordens como melhores preços, e modela explicitamente as cotações do bid e ask na presença de liquidez oculta. E por ultimo, propomos um modelo alternativo para a dinâmica do preço e do spread no limit order book, estudamos o comportamento assintótico do modelo e estabelecemos condições de ergodicidade e transitoridade. Além disso, consideramos a uma família de cadeias de Markov definidos nas sequências de caracteres (strings, ou palavras) com infinito alfabeto e para alguns exemplos inspirados nos modelos de negociações em alta frequência, obtemos condições para ergodicidade, transitoriedade e recorrência nula, para a qual usamos as técnicas de construção de funções Lyapunov. / In this work, we present a set of empirical facts and statistical properties of negotiations at high frequency and discuss some general issues common to high-frequency data such: as discretization, irregular spacing, correlated durations, daily periodicity, temporal correlations and the statistical properties of flows orders. Soon we present two models stylized in the literature for the dynamic limit order book. In the first model the order flow described by separate Poisson processes and we propose it to an alternative form of test ergodicity based on Lyapunov function. The second model is a reduced model that takes into consideration diffusion-type dynamics for the sizes of the bid and ask, and focus only on orders as best price and model explicitly quotes the bid and ask in the presence of hidden liquidity. And finally, we propose an alternative model for the price dynamics and spread in the limit order book, we study the asymptotic behavior of the model and established conditions of ergodicity. Furthermore, we consider the a family of Markov chains defined on the sequences of characters (strings, or words) with infinite alphabet. For some examples inspired by the models of high frequency trading we obtain a conditions for ergodicity, transience and null-recurrence. In order to prove this we use the construction of Lyapunov functions techniques.

[pt] A hipótese de normalidade é comumente utilizada na área de análise de risco para descrever as distribuições dos retornos padronizados pelas volatilidades. No entanto, utilizando cinco dos ativos mais líquidos na Bovespa, este trabalho mostra que tal hipótese não é compatível com medidas de volatilidades estimadas pela metodologia EWMA ou modelos GARCH. Em contraposição, ao extrair a informação contida em cotações intradiárias, a metodologia de volatilidade realizada origina retornos padronizados normais, potencializando ganhos no cálculo de medidas de Valor em Risco. Além disso, são caracterizadas as distribuições de volatilidades e correlações de ativos brasileiros e, em especial, mostra-se que as distribuições das volatilidades são aproximadamente lognormais, enquanto as distribuições das correlações são aproximadamente normais. A análise é feita tanto de um ponto de vista univariado quanto multivariado e fornece subsídio para a melhor modelagem de variâncias e correlações em um contexto de grande dimensionalidade. / [en] The normality assumption is commonly used in the risk management area to describe the distributions of returns standardized by volatilities. However, using five of the most actively traded stocks in Bovespa, this paper shows that this assumption is not compatible with volatilities estimated by EWMA or GARCH models. In sharp contrast, when we use the information contained in high frequency data to construct the realized volatilies measures, we attain the normality of the standardized returns, giving promise of improvements in Value at Risk statistics. We also describe the distributions of volatilities and correlations of the brazilian stocks, showing that the distributions of volatilities are nearly lognormal and the distribuitions of correlations are nearly Gaussian. All analysis is traced both in a univariate and a multivariate framework and provides background for improved high-dimensional volatility and correlation modelling in the brazilian stock market.