This work combines discrete and continuous methods while modeling connect- edness of financial tick data. As discrete method we are using vector autore- gression. For continuous domain Hawkes process is used, which is special case of point process. We found out that financial assets are connected in non- symmetrical fashion. By using two methodologies we were able to model bet- ter how are the series connected. We confirmed existence of price leader in our three stock portfolio and modeled connectedness of jumps between stocks. As conclusion we state that both methods yields important results about price nature on the market and should be used together or at least with awareness of second approach. JEL Classification C32, G11, G14 Keywords Vector Autoregression, Hawkes process, High- frequency analysis, Connectedness Author's e-mail petr.petras@email.cz Supervisor's e-mail krehlik@utia.cas.cz

Within the quantitative financial community there are a lot of different approaches in forming profitable trading strategies. This is frequently performed by analyzing historical prices from different perspectives. Some have analyzed other factors than price that might provide insight in which way the market is heading, which in some cases have been successful. This thesis investigates if a news flow model based on a multivariate Hawkes process could give a peek into the future news flow, and if it can be used to successfully predict financial market movements in terms of logarithmic returns by utilizing regression and classification models such as support vector machines. The results show that the trained models perform poorly in general in terms of common regression and classification metrics. Applying the trained models in simple trading strategies show that in some cases they perform better than a buy-and-hold strategy. The ambiguous results indicate that the models might be profitable in trading strategies, but that the predictions might not be very reliable. The trained models cannot seem to find important structures in the predicted news flow relating to market returns, but before dismissing the news flow model entirely it might altered in some sense by, e.g., expanding the dataset with more observations and by looking at other granularities of time. / Kvantitativa analytiker inom finansvärlden försöker med olika tillvägagångssätt utforma vinnande trading-strategier. Oftast görs detta genom att analysera historiska priser från olika perspektiv. Vissa har analyserat andra faktorer än prisrelaterade sådana, i hopp om att dessa ska ge insikt om vart marknaden är på väg, som i vissa fall har lyckats. Det här arbetet undersöker om en nyhetsflödesmodell baserad på en multivariat Hawkes-process kan ge en inblick i det framtida nyhetsflödet, och om det kan användas för att lyckosamt prediktera finansiella marknaders rörelser i termer av logaritmisk avkastning genom att nyttja regressions- och klassificeringsmodeller. Resultaten visar att de tränade modellerna generellt sett presterar dåligt i termer av vanliga regressions- och klassificeringsmått. Genom att applicera de tränade modellerna till enkelt utformade trading-strategier visas att i vissa fall kan dessa prestera bättre än en buy-and-hold-strategi. De tvetydiga resultaten indikerar att modellerna kan vara lönsamma, men att prediktionerna inte är särskilt pålitliga. De tränade modellerna verkar inte kunna finna viktiga strukturer i data från nyhetsflödesmodellen som relaterar till marknadsavkastningar, men innan nyhetflödesmodellen avfärdas skulle den kunna modifieras genom att, t. ex., utöka antalet observationer, och genom att undersöka andra tidsgranulariteter.

Indiana University-Purdue University Indianapolis (IUPUI) / Temporal point processes (TPP) are mathematical approaches for modeling asynchronous event sequences by considering the temporal dependency of each event on past events and its instantaneous rate. Temporal point processes can model various problems, from earthquake aftershocks, trade orders, gang violence, and reported crime patterns, to network analysis, infectious disease transmissions, and virus spread forecasting. In each of these cases, the entity’s behavior with the corresponding information is noted over time as an asynchronous event sequence, and the analysis is done using temporal point processes, which provides a means to define the generative mechanism of the sequence of events and ultimately predict events and investigate causality. Among point processes, Hawkes process as a stochastic point process is able to model a wide range of contagious and self-exciting patterns. One of Hawkes process’s well-known applications is predicting the evolution of viral processes on networks, which is an important problem in biology, the social sciences, and the study of the Internet. In existing works, mean-field analysis based upon degree distribution is used to predict viral spreading across networks of different types. However, it has been shown that degree distribution alone fails to predict the behavior of viruses on some real-world networks. Recent attempts have been made to use assortativity to address this shortcoming. This thesis illustrates how the evolution of such a viral process is sensitive to the underlying network’s structure. In Chapter 3 , we show that adding assortativity does not fully explain the variance in the spread of viruses for a number of real-world networks. We propose using the graphlet frequency distribution combined with assortativity to explain variations in the evolution of viral processes across networks with identical degree distribution. Using a data-driven approach, by coupling predictive modeling with viral process simulation on real-world networks, we show that simple regression models based on graphlet frequency distribution can explain over 95% of the variance in virality on networks with the same degree distribution but different network topologies. Our results highlight the importance of graphlets and identify a small collection of graphlets that may have the most significant influence over the viral processes on a network. Due to the flexibility and expressiveness of deep learning techniques, several neural network-based approaches have recently shown promise for modeling point process intensities. However, there is a lack of research on the possible adversarial attacks and the robustness of such models regarding adversarial attacks and natural shocks to systems. Furthermore, while neural point processes may outperform simpler parametric models on in-sample tests, how these models perform when encountering adversarial examples or sharp non-stationary trends remains unknown. In Chapter 4 , we propose several white-box and black-box adversarial attacks against deep temporal point processes. Additionally, we investigate the transferability of whitebox adversarial attacks against point processes modeled by deep neural networks, which are considered a more elevated risk. Extensive experiments confirm that neural point processes are vulnerable to adversarial attacks. Such a vulnerability is illustrated both in terms of predictive metrics and the effect of attacks on the underlying point process’s parameters. Expressly, adversarial attacks successfully transform the temporal Hawkes process regime from sub-critical to into a super-critical and manipulate the modeled parameters that is considered a risk against parametric modeling approaches. Additionally, we evaluate the vulnerability and performance of these models in the presence of non-stationary abrupt changes, using the crimes and Covid-19 pandemic dataset as an example. Considering the security vulnerability of deep-learning models, including deep temporal point processes, to adversarial attacks, it is essential to ensure the robustness of the deployed algorithms that is despite the success of deep learning techniques in modeling temporal point processes. In Chapter 5 , we study the robustness of deep temporal point processes against several proposed adversarial attacks from the adversarial defense viewpoint. Specifically, we investigate the effectiveness of adversarial training using universal adversarial samples in improving the robustness of the deep point processes. Additionally, we propose a general point process domain-adopted (GPDA) regularization, which is strictly applicable to temporal point processes, to reduce the effect of adversarial attacks and acquire an empirically robust model. In this approach, unlike other computationally expensive approaches, there is no need for additional back-propagation in the training step, and no further network isrequired. Ultimately, we propose an adversarial detection framework that has been trained in the Generative Adversarial Network (GAN) manner and solely on clean training data. Finally, in Chapter 6 , we discuss implications of the research and future research directions.

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Indiana University-Purdue University Indianapolis (IUPUI) / The counting process is the fundamental of many real-world problems with event data. Poisson process, used as the background intensity of Hawkes process, is the most commonly used point process. The Hawkes process, a self-exciting point process fits to temporal event data, spatial-temporal event data, and event data with covariates. We study the Hawkes process that fits to heterogeneous drug overdose data via a novel semi-parametric approach. The counting process is also related to survival data based on the fact that they both study the occurrences of events over time. We fit a Cox model to temporal event data with a large corpus that is processed into high dimensional covariates. We study the significant features that influence the intensity of events.

We introduce a financial model for limit order book with two main features: First, the limit orders and market orders for the given asset both appear and interact with each other. Second, the high frequency trading (HFT, for short) activities are allowed and described by the scaling limit of nearly-unstable multi-dimensional Hawkes processes with power law decay. The model eventually becomes a stochastic partial differential equation (SPDE, for short) with the diffusion coefficient determined by a Volterra integral equation governed by a Hawkes process, whose Hurst exponent is less than 1/2, which makes the volatility path of the stochastic PDE rougher than that driven by a Brownian motion. We have further established the well-posedness of such a system so that a foundation is laid down for further studies in this direction.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第25091号 / 理博第4998号 / 新制||理||1714(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 日野 正訓, 教授 COLLINSBenoit Vincent Pierre, 教授 楠岡 誠一郎 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DFAM

Le but de cette thèse est de répondre au vrai besoin de prédire les fluctuations futures des prix d'actions. En effet, l'aléatoire régissant ces fluctuations constitue pour des acteurs de la finance, tels que les Market Maker, une des plus grandes sources de risque. Tout au long de cette étude, nous mettons en évidence la possibilité de réduire l'incertitude sur les prix futurs par l'usage des modèles mathématiques appropriés. Cette étude est rendue possible grâce à une grande base de données financières et une puissante grille de calcul mises à notre disposition par l'équipe Automatic Market Making de BNP Paribas. Dans ce document, nous présentons uniquement les résultats de la recherche concernant le trading haute fréquence. Les résultats concernant la partie basse fréquence présentent un intérêt scientifique moindre pour le monde académique et rentrent par ailleurs dans le cadre des résultats confidentiels. Ces résultats seront donc volontairement omis.Dans le premier chapitre, nous présentons le contexte et les objectifs de cette étude. Nous présentons, également, les différentes méthodes utilisées, ainsi que les principaux résultats obtenus. Dans le chapitre 2, nous nous intéressons à l'apport de la supériorité technologique en trading haute fréquence. Dans ce but, nous simulons un trader ultra rapide, omniscient, et agressif, puis nous calculons son gain total sur 3 ans. Les gains obtenus sont très modestes et reflètent l'apport limité de la technologie en trading haute fréquence. Ce résultat souligne l'intérêt primordial de la recherche et de la modélisation dans ce domaine.Dans le chapitre 3, nous étudions la prédictibilité des prix à partir des indicateurs de carnet d'ordre. Nous présentons, à l'aide des espérances conditionnelles, des preuves empiriques de dépendances statistiques entre les prix et les différents indicateurs. L'importance de ces dépendances résulte de la simplicité de la méthode, éliminant tout risque de surapprentissage des données. Nous nous intéressons, ensuite, à la combinaison des différents indicateurs par une régression linéaire et nous analysons les différents problèmes numériques et statistiques liés à cette méthode. Enfin, nous concluons que les prix sont prédictibles pour un horizon de quelques minutes et nous mettons en question l'hypothèse de l'efficience du marché.Dans le chapitre 4, nous nous intéressons au mécanisme de formation du prix à partir des arrivés des évènements dans le carnet d'ordre. Nous classifions les ordres en douze types dont nous analysons les propriétés statistiques. Nous étudions par la suite les dépendances entre ces différents types d'ordres et nous proposons un modèle de carnet d'ordre en ligne avec les observations empiriques. Enfin, nous utilisons ce modèle pour prédire les prix et nous appuyons l'hypothèse de la non-efficience des marchés, suggérée au chapitre 3. / The aim of this thesis is to address the real need of predicting the prices of stocks. In fact, the randomness governing the evolution of prices is, for financial players like market makers, one of the largest sources of risk. In this context, we highlight the possibility of reducing the uncertainty of the future prices using appropriate mathematical models. This study was made possible by a large base of high frequency data and a powerful computational grid provided by the Automatic Market Making team at BNP Paribas. In this paper, we present only the results of high frequency tests. Tests are of less scientific interest in the academic world and are confidential. Therefore, these results will be deliberately omitted.In the first chapter, the background and the objectives of this study are presented along with the different methods used and the main results obtained.The focus of chapter 2 is on the contribution of technological superiority in high frequency trading. In order to do this, an omniscient trader is simulated and the total gain over three years is calculated. The obtained gain is very modest and reflects the limited contribution of technology in high frequency trading. This result underlines the primary role of research and modeling in this field.In Chapter 3, the predictability of prices using some order book indicators is studied. Using conditional expectations, the empirical evidence of the statistical dependencies between the prices and indicators is presented. The importance of these dependencies results from the simplicity of the method, eliminating any risk of over fitting the data. Then the combination of the various indicators is tested using a linear regression and the various numerical and statistical problems associated with this method are analyzed. Finally, it can be concluded that the prices are predictable for a period of a few minutes and the assumption of market efficiency is questioned.In Chapter 4, the mechanism of price formation from the arrival of events in the order book is investigated. The orders are classified in twelve types and their statistical properties are analyzed. The dependencies between these different types of orders are studied and a model of order book in line with the empirical observations is proposed. Finally, this model is used to predict prices and confirm the assumption of market inefficiency suggested in Chapter 3.

Indiana University-Purdue University Indianapolis (IUPUI) / Many complex processes can be viewed as sequential events on a network. In this thesis, we study the interplay between a network and the event sequences on it. We first focus on predicting events on a known network. Examples of such include: modeling retweet cascades, forecasting earthquakes, and tracing the source of a pandemic. In specific, given the network structure, we solve two types of problems - (1) forecasting future events based on the historical events, and (2) identifying the initial event(s) based on some later observations of the dynamics. The inverse problem of inferring the unknown network topology or links, based on the events, is also of great important. Examples along this line include: constructing influence networks among Twitter users from their tweets, soliciting new members to join an event based on their participation history, and recommending positions for job seekers according to their work experience. Following this direction, we study two types of problems - (1) recovering influence networks, and (2) predicting links between a node and a group of nodes, from event sequences.

Accurate forecasting of stock price movements is crucial for optimizing trade execution and mitigating risk in automated trading environments, especially when leveraging Limit Order Book (LOB) data. However, developing predictive models from LOB data presents substantial challenges due to its inherent complexities and high-frequency nature. In this thesis, the application of the General Compound Hawkes Process (GCHP) is explored to predict price volatility. Within this framework, a Hawkes process is employed to estimate the times of price changes, and a Markovian model is utilized to determine their amplitudes. The price volatility is obtained through both numerical and analytical methodologies. The performance of the GCHP is assessed on a publicly available dataset, including five distinct stocks. To enhance accuracy, the number of states in the Markov chain is gradually increased, and the advantages of incorporating a higher-order Markov chain for refined volatility estimation are demonstrated.