A importância de se considerar os volumes na análise dos movimentos de preços de ações pode ser considerada uma prática bastante aceita na área financeira. No entanto, quando se olha para a produção científica realizada neste campo, ainda não é possível encontrar um modelo unificado que inclua os volumes e as variações de preços para fins de análise de preços de ações. Neste trabalho é apresentado um modelo computacional que pode preencher esta lacuna, propondo um novo índice para analisar o preço das ações com base em seus históricos de preços e volumes negociados. O objetivo do modelo é o de estimar as atuais proporções do volume total de papéis negociados no mercado de uma ação (free float) distribuídos de acordo com os seus respectivos preços passados de compra. Para atingir esse objetivo, foi feito uso da modelagem dinâmica financeira aplicada a dados reais da bolsa de valores de São Paulo (Bovespa) e também a dados simulados por meio de um modelo de livro de ordens (order book). O valor do índice varia de acordo com a diferença entre a atual porcentagem do total de papéis existentes no mercado que foram comprados no passado a um preço maior do que o preço atual da ação e a sua respectiva contrapartida, que seria a atual porcentagem de papéis existentes no mercado que foram comprados no passado a um preço menor do que o preço atual da ação. Apesar de o modelo poder ser considerado matematicamente bastante simples, o mesmo foi capaz de melhorar significativamente a performance financeira de agentes operando com dados do mercado real e com dados simulados, o que contribui para demonstrar a sua racionalidade e a sua aplicabilidade. Baseados nos resultados obtidos, e também na lógica bastante intuitiva que está por trás deste modelo, acredita-se que o índice aqui proposto pode ser bastante útil na tarefa de ajudar os investidores a definir intervalos ideais para compra e venda de ações no mercado financeiro. / The importance of considering the volumes to analyze stock prices movements can be considered as a well-accepted practice in the financial area. However, when we look at the scientific production in this field, we still cannot find a unified model that includes volume and price variations for stock prices assessment purposes. In this paper we present a computer model that could fulfill this gap, proposing a new index to evaluate stock prices based on their historical prices and volumes traded. The aim of the model is to estimate the current proportions of the total volume of shares available in the market from a stock distributed according with their respective prices traded in the past. In order to do so, we made use of dynamic financial modeling and applied it to real financial data from the Sao Paulo Stock Exchange (Bovespa) and also to simulated data which was generated trough an order book model. The value of our index varies based on the difference between the current proportion of shares traded in the past for a price above the current price of the stock and its respective counterpart, which would be the proportion of shares traded in the past for a price below the current price of the stock. Besides the model can be considered mathematically very simple, it was able to improve significantly the financial performance of agents operating with real market data and with simulated data, which contributes to demonstrate its rationale and its applicability. Based on the results obtained, and also on the very intuitive logic of our model, we believe that the index proposed here can be very useful to help investors on the activity of determining ideal price ranges for buying and selling stocks in the financial market.

A importância de se considerar os volumes na análise dos movimentos de preços de ações pode ser considerada uma prática bastante aceita na área financeira. No entanto, quando se olha para a produção científica realizada neste campo, ainda não é possível encontrar um modelo unificado que inclua os volumes e as variações de preços para fins de análise de preços de ações. Neste trabalho é apresentado um modelo computacional que pode preencher esta lacuna, propondo um novo índice para analisar o preço das ações com base em seus históricos de preços e volumes negociados. O objetivo do modelo é o de estimar as atuais proporções do volume total de papéis negociados no mercado de uma ação (free float) distribuídos de acordo com os seus respectivos preços passados de compra. Para atingir esse objetivo, foi feito uso da modelagem dinâmica financeira aplicada a dados reais da bolsa de valores de São Paulo (Bovespa) e também a dados simulados por meio de um modelo de livro de ordens (order book). O valor do índice varia de acordo com a diferença entre a atual porcentagem do total de papéis existentes no mercado que foram comprados no passado a um preço maior do que o preço atual da ação e a sua respectiva contrapartida, que seria a atual porcentagem de papéis existentes no mercado que foram comprados no passado a um preço menor do que o preço atual da ação. Apesar de o modelo poder ser considerado matematicamente bastante simples, o mesmo foi capaz de melhorar significativamente a performance financeira de agentes operando com dados do mercado real e com dados simulados, o que contribui para demonstrar a sua racionalidade e a sua aplicabilidade. Baseados nos resultados obtidos, e também na lógica bastante intuitiva que está por trás deste modelo, acredita-se que o índice aqui proposto pode ser bastante útil na tarefa de ajudar os investidores a definir intervalos ideais para compra e venda de ações no mercado financeiro. / The importance of considering the volumes to analyze stock prices movements can be considered as a well-accepted practice in the financial area. However, when we look at the scientific production in this field, we still cannot find a unified model that includes volume and price variations for stock prices assessment purposes. In this paper we present a computer model that could fulfill this gap, proposing a new index to evaluate stock prices based on their historical prices and volumes traded. The aim of the model is to estimate the current proportions of the total volume of shares available in the market from a stock distributed according with their respective prices traded in the past. In order to do so, we made use of dynamic financial modeling and applied it to real financial data from the Sao Paulo Stock Exchange (Bovespa) and also to simulated data which was generated trough an order book model. The value of our index varies based on the difference between the current proportion of shares traded in the past for a price above the current price of the stock and its respective counterpart, which would be the proportion of shares traded in the past for a price below the current price of the stock. Besides the model can be considered mathematically very simple, it was able to improve significantly the financial performance of agents operating with real market data and with simulated data, which contributes to demonstrate its rationale and its applicability. Based on the results obtained, and also on the very intuitive logic of our model, we believe that the index proposed here can be very useful to help investors on the activity of determining ideal price ranges for buying and selling stocks in the financial market.

Market making – the process of simultaneously and continuously providing buy and sell prices in a financial asset – is rather complicated to optimize. Applying reinforcement learning (RL) to infer optimal market making strategies is a relatively uncharted and novel research area. Most published articles in the field are notably opaque concerning most aspects, including precise methods, parameters, and results. This thesis attempts to explore and shed some light on the techniques, problem formulations, algorithms, and hyperparameters used to construct RL-derived strategies for market making. First, a simple probabilistic model of a limit order book is used to compare analytical and RL-derived strategies. Second, a market making agent is trained on a more complex Markov chain model of a limit order book using tabular Q-learning and deep reinforcement learning with double deep Q-learning. Results and strategies are analyzed, compared, and discussed. Finally, we propose some exciting extensions and directions for future work in this research field. / Likviditetsgarantering (eng. ”market making”) – processen att simultant och kontinuerligt kvotera köp- och säljpriser i en finansiell tillgång – är förhållandevis komplicerat att optimera. Att använda förstärkningsinlärning (eng. ”reinforcement learning”) för att härleda optimala strategier för likviditetsgarantering är ett relativt outrett och nytt forskningsområde. De flesta publicerade artiklarna inom området är anmärkningsvärt återhållsamma gällande detaljer om de tekniker, problemformuleringar, algoritmer och hyperparametrar som används för att framställa förstärkningsinlärningsbaserade strategier. I detta examensarbete så gör vi ett försök på att utforska och bringa klarhet över dessa punkter. Först används en rudimentär probabilistisk modell av en limitorderbok som underlag för att jämföra analytiska och förstärkningsinlärda strategier. Därefter brukas en mer sofistikerad Markovkedjemodell av en limitorderbok för att jämföra tabulära och djupa inlärningsmetoder. Till sist presenteras även spännande utökningar och direktiv för framtida arbeten inom området.

Limit-Orderbücher sind das Standardinstrument der Preisbildung in modernen Finanzmärkten. Während Strom traditionell in Auktionen gehandelt wird, gibt es Intraday Strommärkte wie beispielsweise den SIDC-Markt, in welchem Käufer und Verkäufer über Limit-Orderbücher zusammentreffen. In dieser Arbeit werden wir stochastische Modelle von Limit-Orderbüchern auf der Grundlage der zugrundeliegenden Marktmikrostruktur entwickeln. Einen besonderen Schwerpunkt legen wir dabei auf die Berücksichtigung besonderer Merkmale der Intraday-Strommärkte, die sich zum Teil deutlich von denen der Finanzmärkte unterscheiden. Die in dieser Arbeit entwickelten Modelle beginnen mit einer realistischen und mikroskopischen Beschreibung der Marktdynamik. Große Preisänderungen über kurze Zeiträume werden ebenso berücksichtigt wie begrenzte grenzüberschreitende Aktivitäten. Diese mikroskopischen Modelle sind im Allgemeinen zu rechenintensiv für praktische Anwendungen. Das Hauptziel dieser Arbeit ist es daher, geeignete Approximationen dieser mikroskopischen Modelle durch sogenannte Skalierungsgrenzprozesse herzuleiten. Zu diesem Zweck werden sorgfältig Skalierungsannahmen formuliert und in die mikroskopischen Modelle eingebaut. Diese Annahmen ermöglichen es uns, ihr Hochfrequenzverhalten zu untersuchen, vorausgesetzt, dass die Größe eines einzelnen Auftrags gegen Null konvergiert, während die Auftragseingangsrate gegen unendlich tendiert. Die Kalibrierung mathematischer Modelle ist aus Anwendersicht eines der Hauptanliegen. Dabei ist bekannt, dass Änderungspunkte (abrupte Schwankungen) in hochfrequenten Finanzdaten vorhanden sind. Falls sie durch endogene Effekte verursacht wurden, muss bei der Schätzung solcher Änderungspunkte die Abhängigkeit von den zugrundeliegenden Daten berücksichtigt werden. Daher erweitern wir im letzten Teil dieser Arbeit die bestehende Literatur zur Erkennung von Änderungspunkten, so dass auch zufällige, von den Daten abhängige Änderungspunkte gehandhabt werden können. / Limit order books are the standard instrument for price formation in modern financial markets. While electricity has traditionally been traded through auctions, there are intraday electricity markets, such as the SIDC market, in which buyers and sellers meet via limit order books. In this thesis, stochastic models of limit order books are developed based on the underlying market microstructure. A particular focus is set on incorporating unique characteristics of intraday electricity markets, some of which are quite different from those of financial markets. The developed models in this thesis start with a realistic and microscopic description of the market dynamics. Large price changes over short time periods are considered, as well as limited cross-border activities. These microscopic models are generally computationally too intensive for practical applications. The main goal of this thesis is therefore to derive suitable approximations of these microscopic models by so-called scaling limits. For this purpose, appropriate scaling assumptions are carefully formulated and incorporated into the microscopic models which allow us to study their high-frequency behavior when the size of an individual order converges to zero while the order arrival rate tends to infinity. Calibration of mathematical models is one of the main concerns from a practitioner’s point of view. It is well known that change points (abrupt variations) are present in high-frequency financial data. If they are caused by endogenous effects, the dependence on the underlying data must be considered when estimating such change points. In the final part of this thesis, we extend the existing literature on change point detection so that random change points depending on the data can also be handled.