Three Essays on Financial Risks Using High Frequency Data

Le sujet général de cette thèse est le risque financier dans un contexte de disponibilité des données à hautes fréquences, avec un accent particulier sur le risque systémique, le risque des portefeuilles de grande dimension et le bruit de microstructure. Elle s’articule en trois principaux chapitres. Le premier chapitre propose un modèle de forme réduite, à temps continu, afin de caractériser la propagation des chocs idiosyncratiques négatifs à l’intérieur d’un ensemble de plusieurs entités financières. En utilisant un modèle à facteurs avec des sauts mutuellement excités, à la fois sur les prix et la volatilité, nous distinguons différentes sources de transmission de chocs financiers telles que la corrélation, la connectivité et la contagion. La stratégie d’estimation repose sur la méthode des moments généralisés et tire profit de la disponibilité des données à très haute fréquence. Nous utilisons certains paramètres spécifiques du modèle pour définir des réseaux pondérés pour la transmission des chocs. Aussi, nous fournissons de nouvelles mesures de fragilité du système financier. Nous construisons des cartes de propagation des chocs, d’abord pour certaines banques et compagnies d’assurance clés aux USA, et ensuite pour les neuf plus grands secteurs de l’économie américaine. Il en sort qu’au-delà des facteurs communs, les chocs financés se propagent via deux canaux distincts et complémentaires : les prix et la volatilité. Dans le deuxième chapitre, nous développons un nouvel estimateur de la matrice de covolatilité réalisée, applicable dans les situations où le nombre d’actifs est grand et les données à haute fréquence sont contaminées par des bruits de microstructure. Notre estimateur repose sur l’hypothèse d’une structure factorielle de la composante du bruit, distincte des facteurs de risque systématiques latents qui caractérisent la variation transversale des rendements.Le nouvel estimateur fournit des estimations théoriquement plus efficientes et plus précises en échantillon fini, relativement aux autres méthodes d’estimation récentes. Les résultats théoriques et basés sur des simulations sont corroborés par une application empirique liée à l’allocation de portefeuille et à la minimisation du risque impliquant plusieurs centaines d’actions individuelles. Le dernier chapitre présente une méthodologie permettant d’estimer les caractéristiques du bruit de microstructure et les rendements latents dans une configuration à grande dimension. Nous nous appuyons sur des hypothèses factorielles tant sur les rendements latents que sur le bruit de microstructure. La procédure est capable d’estimer les rotations des facteurs communs, les coefficients de charge et les volatilités du bruit de microstructure pour un grand nombre d’actifs. En utilisant les actions incluses dans le S & P500 au cours de la période allant de janvier 2007 à décembre 2011, nous estimons les facteurs communs du bruit de microstructure et les comparons à certaines mesures de liquidité à l’échelle du marché, calculées à partir de variables financières réelles. Il en résulte que : le premier facteur est corrélé au spread moyen et au nombre moyen d’actions en circulation ; les deuxième et troisième facteurs sont uniquement liés au spread ; les quatrième et cinquième facteurs varient significativement avec le prix moyen des actions à la fermeture. De plus, les volatilités des facteurs du bruit de microstructure s’expliquent largement par le spread moyen, le volume moyen, le nombre moyen de transactions et la taille moyenne desdites transactions.This thesis is about financial risks and high frequency data, with a particular focus on financial systemic risk, the risk of high dimensional portfolios and market microstructure noise. It is organized on three chapters. The first chapter provides a continuous time reduced-form model for the propagation of negative idiosyncratic shocks within a financial system. Using common factors and mutually exciting jumps both in price and volatility, we distinguish between sources of systemic failure such as macro risk drivers, connectedness and contagion. The estimation procedure relies on the GMM approach and takes advantage of high frequency data. We use models’ parameters to define weighted, directed networks for shock transmission, and we provide new measures for the financial system fragility. We construct paths for the propagation of shocks, firstly within a number of key US banks and insurance companies, and secondly within the nine largest S&P sectors during the period 2000-2014. We find that beyond common factors, systemic dependency has two related but distinct channels: price and volatility jumps. In the second chapter, we develop a new factor-based estimator of the realized covolatility matrix, applicable in situations when the number of assets is large and the high-frequency data are contaminated with microstructure noises. Our estimator relies on the assumption of a factor structure for the noise component, separate from the latent systematic risk factors that characterize the cross-sectional variation in the frictionless returns. The new estimator provides theoretically more efficient and finite-sample more accurate estimates of large-scale integrated covolatility, correlation, and inverse covolatility matrices than other recently developed realized estimation procedures. These theoretical and simulation-based findings are further corroborated by an empirical application related to portfolio allocation and risk minimization involving several hundred individual stocks. The last chapter presents a factor-based methodology to estimate microstructure noise characteristics and frictionless prices under a high dimensional setup. We rely on factor assumptions both in latent returns and microstructure noise. The methodology is able to estimate rotations of common factors, loading coefficients and volatilities in microstructure noise for a huge number of stocks. Using stocks included in the S&P500 during the period spanning January 2007 to December 2011, we estimate microstructure noise common factors and compare them to some market-wide liquidity measures computed from real financial variables. We obtain that: the first factor is correlated to the average spread and the average number of shares outstanding; the second and third factors are related to the spread; the fourth and fifth factors are significantly linked to the closing log-price. In addition, volatilities of microstructure noise factors are widely explained by the average spread, the average volume, the average number of trades and the average trade size

Principal Component Analysis in Financial Data Science

Numerous methods exist aimed at examining patterns in structured and unstructured financial data. Applications of these methods include fraud detection, risk management, credit allocation, assessment of the risk of default, customer analytics, trading prediction, and many others, creating a broad field of research named Financial data science. A problem within the field that remains significantly under-researched, yet very important, is that of differentiating between the three major types of business activities—merchandising, manufacturing, and service based on the structured data available in financial reports. It can be argued that, due to the inherent idiosyncrasies of the three types of business activities, methods for assessment of the risk of default, methods for credit allocation, and methods for fraud detection would all see an improved performance if reliable information on the percentage of entities’ business activities allocated to the three major activities would be available. To this end, in this paper, we propose a clustering procedure that relies on Principal Component Analysis (PCA) for dimensionality reduction and feature selection. The procedure is presented using a large empirical data set comprising complete financial reports for various business entities operating in the Republic in Serbia, that pertain to the reporting period 2019

An efficient polynomial chaos-based proxy model for history matching and uncertainty quantification of complex geological structures

A novel polynomial chaos proxy-based history matching and uncertainty quantification method is presented that can be employed for complex geological structures in inverse problems. For complex geological structures, when there are many unknown geological parameters with highly nonlinear correlations, typically more than 106 full reservoir simulation runs might be required to accurately probe the posterior probability space given the production history of reservoir. This is not practical for high-resolution geological models. One solution is to use a "proxy model" that replicates the simulation model for selected input parameters. The main advantage of the polynomial chaos proxy compared to other proxy models and response surfaces is that it is generally applicable and converges systematically as the order of the expansion increases. The Cameron and Martin theorem 2.24 states that the convergence rate of the standard polynomial chaos expansions is exponential for Gaussian random variables. To improve the convergence rate for non-Gaussian random variables, the generalized polynomial chaos is implemented that uses an Askey-scheme to choose the optimal basis for polynomial chaos expansions [199]. Additionally, for the non-Gaussian distributions that can be effectively approximated by a mixture of Gaussian distributions, we use the mixture-modeling based clustering approach where under each cluster the polynomial chaos proxy converges exponentially fast and the overall posterior distribution can be estimated more efficiently using different polynomial chaos proxies. The main disadvantage of the polynomial chaos proxy is that for high-dimensional problems, the number of the polynomial chaos terms increases drastically as the order of the polynomial chaos expansions increases. Although different non-intrusive methods have been developed in the literature to address this issue, still a large number of simulation runs is required to compute high-order terms of the polynomial chaos expansions. This work resolves this issue by proposing the reduced-terms polynomial chaos expansion which preserves only the relevant terms in the polynomial chaos representation. We demonstrated that the sparsity pattern in the polynomial chaos expansion, when used with the Karhunen-Loéve decomposition method or kernel PCA, can be systematically captured. A probabilistic framework based on the polynomial chaos proxy is also suggested in the context of the Bayesian model selection to study the plausibility of different geological interpretations of the sedimentary environments. The proposed surrogate-accelerated Bayesian inverse analysis can be coherently used in practical reservoir optimization workflows and uncertainty assessments

A Survey on Quantum Computational Finance for Derivatives Pricing and VaR

[Abstract]: We review the state of the art and recent advances in quantum computing applied to derivative pricing and the computation of risk estimators like Value at Risk. After a brief description of the financial derivatives, we first review the main models and numerical techniques employed to assess their value and risk on classical computers. We then describe some of the most popular quantum algorithms for pricing and VaR. Finally, we discuss the main remaining challenges for the quantum algorithms to achieve their potential advantages.Xunta de Galicia; ED431G 2019/01All authors acknowledge the European Project NExt ApplicationS of Quantum Computing (NEASQC), funded by Horizon 2020 Program inside the call H2020-FETFLAG-2020-01 (Grant Agreement 951821). Á. Leitao, A. Manzano and C. Vázquez wish to acknowledge the support received from the Centro de Investigación de Galicia “CITIC”, funded by Xunta de Galicia and the European Union (European Regional Development Fund- Galicia 2014-2020 Program), by Grant ED431G 2019/01

Machine Learning in Orbit Estimation: a Survey

Since the late '50s, when the first artificial satellite was launched, the number of resident space objects (RSOs) has steadily increased. It is estimated that around 1 Million objects larger than 1 cm are currently orbiting the Earth, with only 30,000, larger than 10 cm, presently being tracked. To avert a chain reaction of collisions, termed Kessler Syndrome, it is indispensable to accurately track and predict space debris and satellites' orbit alike. Current physics-based methods have errors in the order of kilometres for 7 days predictions, which is insufficient when considering space debris that have mostly less than 1 meter. Typically, this failure is due to uncertainty around the state of the space object at the beginning of the trajectory, forecasting errors in environmental conditions such as atmospheric drag, as well as specific unknown characteristics such as mass or geometry of the RSO. Leveraging data-driven techniques, namely machine learning, the orbit prediction accuracy can be enhanced: by deriving unmeasured objects' characteristics, improving non-conservative forces' effects, and by the superior abstraction capacity that Deep Learning models have of modelling highly complex non-linear systems. In this survey, we provide an overview of the current work being done in this field.Comment: submitted to AIAA Journal of Guidance, Control and Dynamic

A survey on Bayesian nonparametric learning

© 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM. Bayesian (machine) learning has been playing a significant role in machine learning for a long time due to its particular ability to embrace uncertainty, encode prior knowledge, and endow interpretability. On the back of Bayesian learning's great success, Bayesian nonparametric learning (BNL) has emerged as a force for further advances in this field due to its greater modelling flexibility and representation power. Instead of playing with the fixed-dimensional probabilistic distributions of Bayesian learning, BNL creates a new “game” with infinite-dimensional stochastic processes. BNL has long been recognised as a research subject in statistics, and, to date, several state-of-the-art pilot studies have demonstrated that BNL has a great deal of potential to solve real-world machine-learning tasks. However, despite these promising results, BNL has not created a huge wave in the machine-learning community. Esotericism may account for this. The books and surveys on BNL written by statisticians are overcomplicated and filled with tedious theories and proofs. Each is certainly meaningful but may scare away new researchers, especially those with computer science backgrounds. Hence, the aim of this article is to provide a plain-spoken, yet comprehensive, theoretical survey of BNL in terms that researchers in the machine-learning community can understand. It is hoped this survey will serve as a starting point for understanding and exploiting the benefits of BNL in our current scholarly endeavours. To achieve this goal, we have collated the extant studies in this field and aligned them with the steps of a standard BNL procedure-from selecting the appropriate stochastic processes through manipulation to executing the model inference algorithms. At each step, past efforts have been thoroughly summarised and discussed. In addition, we have reviewed the common methods for implementing BNL in various machine-learning tasks along with its diverse applications in the real world as examples to motivate future studies

Modelling, Simulation and Data Analysis in Acoustical Problems

Modelling and simulation in acoustics is currently gaining importance. In fact, with the development and improvement of innovative computational techniques and with the growing need for predictive models, an impressive boost has been observed in several research and application areas, such as noise control, indoor acoustics, and industrial applications. This led us to the proposal of a special issue about “Modelling, Simulation and Data Analysis in Acoustical Problems”, as we believe in the importance of these topics in modern acoustics’ studies. In total, 81 papers were submitted and 33 of them were published, with an acceptance rate of 37.5%. According to the number of papers submitted, it can be affirmed that this is a trending topic in the scientific and academic community and this special issue will try to provide a future reference for the research that will be developed in coming years