Credit risk & forward price models

Doutoramento em Gestão

Essays in Financial Econometrics

The first paper sheds light on the informational content of high frequency data and daily data. I assess the economic value of the two family models comparing their performance in forecasting asset volatility through the Value at Risk metric. In running the comparison this paper introduces two key assumptions: jumps in prices and leverage effect in volatility dynamics. Findings suggest that high frequency data models do not exhibit a superior performance over daily data models. In the second paper, building on Majewski et al. (2015), I propose an affine-discrete time model, labeled VARG-J, which is characterized by a multifactor volatility specification. In the VARG-J model volatility experiences periods of extreme movements through a jump factor modeled as an Autoregressive Gamma Zero process. The estimation under historical measure is done by quasi-maximum likelihood and the Extended Kalman Filter. This strategy allows to filter out both volatility factors introducing a measurement equation that relates the Realized Volatility to latent volatility. The risk premia parameters are calibrated using call options written on S&P500 Index. The results clearly illustrate the important contribution of the jump factor in the pricing performance of options and the economic significance of the volatility jump risk premia. In the third paper, I analyze whether there is empirical evidence of contagion at the bank level, measuring the direction and the size of contagion transmission between European markets. In order to understand and quantify the contagion transmission on banking market, I estimate the econometric model by Aït-Sahalia et al. (2015) in which contagion is defined as the within and between countries transmission of shocks and asset returns are directly modeled as a Hawkes jump diffusion process. The empirical analysis indicates that there is a clear evidence of contagion from Greece to European countries as well as self-contagion in all countries.

The Hitchin map for one-nodal base curves of compact type

Studying moduli spaces of semistable Higgs bundles (E, \phi) of rank n on a smooth curve C, a key role is played by the spectral curve X (Hitchin), because an important result by Beauville-Narasimhan-Ramanan allows us to study isomorphism classes of such Higgs bundles in terms of isomorphism classes of rank-1 torsion-free sheaves on X. This way, the generic fibre of the Hitchin map, which associates to any semistable Higgs bundle the coefficients of the characteristic polynomial of \phi, is isomorphic to the Jacobian of X. Focusing on rank-2 Higgs data, this construction was extended by Barik to the case in which the curve C is reducible, one-nodal, having two smooth components. Such curve is called of compact type because its Picard group is compact. In this work, we describe and clarify the main points of the construction by Barik and we give examples, especially concerning generic fibres of the Hitchin map. Referring to Hausel-Pauly, we consider the case of SL(2,C)-Higgs bundles on a smooth base curve, which are such that the generic fibre of the Hitchin map is a subvariety of the Jacobian of X, the Prym variety. We recall the description of special loci, called endoscopic loci, such that the associated Prym variety is not connected. Then, letting G be an affine reductive group having underlying Lie algebra so(4,C), we consider G-Higgs bundles on a smooth base curve. Starting from the construction by Bradlow-Schaposnik, we discuss the associated endoscopic loci. By adapting these studies to a one-nodal base curve of compact type, we describe the fibre of the SL(2,C)-Hitchin map and of the G-Hitchin map, together with endoscopic loci. In the Appendix, we give an interpretation of generic spectral curves in terms of families of double covers.

Wireless solutions for the industrial internet of things

The fourth industrial revolution is paving the way for Industrial Internet of Things applications where industrial assets (e.g., robotic arms, valves, pistons) are equipped with a large number of wireless devices (i.e., microcontroller boards that embed sensors and actuators) to enable a plethora of new applications, such as analytics, diagnostics, monitoring, as well as supervisory, and safety control use-cases. Nevertheless, current wireless technologies, such as Wi-Fi, Bluetooth, and even private 5G networks, cannot fulfill all the requirements set up by the Industry 4.0 paradigm, thus opening up new 6G-oriented research trends, such as the use of THz frequencies. In light of the above, this thesis provides (i) a broad overview of the main use-cases, requirements, and key enabling wireless technologies foreseen by the fourth industrial revolution, and (ii) proposes innovative contributions, both theoretical and empirical, to enhance the performance of current and future wireless technologies at different levels of the protocol stack. In particular, at the physical layer, signal processing techniques are being exploited to analyze two multiplexing schemes, namely Affine Frequency Division Multiplexing and Orthogonal Chirp Division Multiplexing, which seem promising for high-frequency wireless communications. At the medium access layer, three protocols for intra-machine communications are proposed, where one is based on LoRa at 2.4 GHz and the others work in the THz band. Different scheduling algorithms for private industrial 5G networks are compared, and two main proposals are described, i.e., a decentralized scheme that leverages machine learning techniques to better address aperiodic traffic patterns, and a centralized contention-based design that serves a federated learning industrial application. Results are provided in terms of numerical evaluations, simulation results, and real-world experiments. Several improvements over the state-of-the-art were obtained, and the description of up-and-running testbeds demonstrates the feasibility of some of the theoretical concepts when considering a real industry plant.

Le Coniche dallo spazio al piano

Questa tesi ha lo scopo di presentare le coniche sotto vari punti di vista: come sezioni coniche, dalla scoperta da parte di Menecmo alla visione di Apollonio nella sua opera "Le Coniche"; come luoghi geometrici; come curve algebriche del secondo ordine, sia dal punto di vista affine sia proiettivo.

Convolutional Neural Network Architectures for Template Matching

The Neural Networks customized and tested in this thesis (WaldoNet, FlowNet and PatchNet) are a first exploration and approach to the Template Matching task. The possibilities of extension are therefore many and some are proposed below. During my thesis, I have analyzed the functioning of the classical algorithms and adapted with deep learning algorithms. The features extracted from both the template and the query images resemble the keypoints of the SIFT algorithm. Then, instead of similarity function or keypoints matching, WaldoNet and PatchNet use the convolutional layer to compare the features, while FlowNet uses the correlational layer. In addition, I have identified the major challenges of the Template Matching task (affine/non-affine transformations, intensity changes...) and solved them with a careful design of the dataset.

An optimal control tool for trajectory generation of autonomous drones

In the recent years, autonomous aerial vehicles gained large popularity in a variety of applications in the field of automation. To accomplish various and challenging tasks the capability of generating trajectories has assumed a key role. As higher performances are sought, traditional, flatness-based trajectory generation schemes present their limitations. In these approaches the highly nonlinear dynamics of the quadrotor is, indeed, neglected. Therefore, strategies based on optimal control principles turn out to be beneficial, since in the trajectory generation process they allow the control unit to best exploit the actual dynamics, and enable the drone to perform quite aggressive maneuvers. This dissertation is then concerned with the development of an optimal control technique to generate trajectories for autonomous drones. The algorithm adopted to this end is a second-order iterative method working directly in continuous-time, which, under proper initialization, guarantees quadratic convergence to a locally optimal trajectory. At each iteration a quadratic approximation of the cost functional is minimized and a decreasing direction is then obtained as a linear-affine control law, after solving a differential Riccati equation. The algorithm has been implemented and its effectiveness has been tested on the vectored-thrust dynamical model of a quadrotor in a realistic simulative setup.

Deep learning based style transfer for low altitude aerial imagery

Unmanned Aerial Vehicle (UAVs) equipped with cameras have been fast deployed to a wide range of applications, such as smart cities, agriculture or search and rescue applications. Even though UAV datasets exist, the amount of open and quality UAV datasets is limited. So far, we want to overcome this lack of high quality annotation data by developing a simulation framework for a parametric generation of synthetic data. The framework accepts input via a serializable format. The input specifies which environment preset is used, the objects to be placed in the environment along with their position and orientation as well as additional information such as object color and size. The result is an environment that is able to produce UAV typical data: RGB image from the UAVs camera, altitude, roll, pitch and yawn of the UAV. Beyond the image generation process, we improve the resulting image data photorealism by using Synthetic-To-Real transfer learning methods. Transfer learning focuses on storing knowledge gained while solving one problem and applying it to a different - although related - problem. This approach has been widely researched in other affine fields and results demonstrate it to be an interesing area to investigate. Since simulated images are easy to create and synthetic-to-real translation has shown good quality results, we are able to generate pseudo-realistic images. Furthermore, object labels are inherently given, so we are capable of extending the already existing UAV datasets with realistic quality images and high resolution meta-data. During the development of this thesis we have been able to produce a result of 68.4% on UAVid. This can be considered a new state-of-art result on this dataset.

Sviluppo di Retrieval-based Chatbot per l'Italiano con Transformer

L’Intelligenza Artificiale negli ultimi anni sta plasmando il futuro dell’umanità in quasi tutti i settori. È già il motore principale di diverse tecnologie emergenti come i big data, la robotica e l’IoT e continuerà ad agire come innovatore tecnologico nel futuro prossimo. Le recenti scoperte e migliorie sia nel campo dell’hardware che in quello matematico hanno migliorato l’efficienza e ridotto i tempi di esecuzione dei software. È in questo contesto che sta evolvendo anche il Natural Language Processing (NLP), un ramo dell’Intelligenza Artificiale che studia il modo in cui fornire ai computer l'abilità di comprendere un testo scritto o parlato allo stesso modo in cui lo farebbe un essere umano. Le ambiguità che distinguono la lingua naturale dalle altre rendono ardui gli studi in questo settore. Molti dei recenti sviluppi algoritmici su NLP si basano su tecnologie inventate decenni fa. La ricerca in questo settore è quindi in continua evoluzione. Questa tesi si pone l'obiettivo di sviluppare la logica di una chatbot help-desk per un'azienda privata. Lo scopo è, sottoposta una domanda da parte di un utente, restituire la risposta associata presente in una collezione domande-risposte. Il problema che questa tesi affronta è sviluppare un modello di NLP in grado di comprendere il significato semantico delle domande in input, poiché esse possono essere formulate in molteplici modi, preservando il contenuto semantico a discapito della sintassi. A causa delle ridotte dimensioni del dataset italiano proprietario su cui testare il modello chatbot, sono state eseguite molteplici sperimentazioni su un ulteriore dataset italiano con task affine. Attraverso diversi approcci di addestramento, tra cui apprendimento metrico, sono state raggiunte alte accuratezze sulle più comuni metriche di valutazione, confermando le capacità del modello proposto e sviluppato.

Gruppi di Galois primitivi ed imprimitivi

L'obiettivo di questa tesi è la caratterizzazione dei gruppi di Galois di alcune classi di polinomi separabili e risolubili per radicali. Questa classificazione si baserà sulle proprietà di primitività e imprimitività di tali gruppi, proprietà che descrivono il carattere della loro azione permutativa sulle radici dei polinomi. Da tale analisi potremo inoltre dedurre importanti informazioni sui polinomi, i quali, a loro volta, saranno detti primitivi o imprimitivi. Dopo aver ricordato alcune definizioni e risultati fondamentali di Teoria di Galois e Teoria dei gruppi, studieremo alcuni gruppi di permutazioni, concentrandoci in particolare sul gruppo lineare affine e sul prodotto intrecciato di due gruppi di permutazioni: tali oggetti costituiscono, infatti, gli strumenti principali per la descrizione dei gruppi di Galois che affronteremo negli ultimi capitoli. Nel Capitolo 3, in particolare, ci concentreremo su polinomi imprimitivi di grado p², con p primo. Nel quarto, invece, dimostreremo un potente Teorema che fornisce una notevole caratterizzazione dei gruppi di Galois di tutti i polinomi primitivi e risolubili per radicali.