The Libor Market Model: from theory to calibration

This thesis is focused on the financial model for interest rates called the LIBOR Market Model. In the appendixes, we provide the necessary mathematical theory. In the inner chapters, firstly, we define the main interest rates and financial instruments concerning with the interest rate models, then, we set the LIBOR market model, demonstrate its existence, derive the dynamics of forward LIBOR rates and justify the pricing of caps according to the Black���s formula. Then, we also present the Swap Market Model, which models the forward swap rates instead of the LIBOR ones. Even this model is justified by a theoretical demonstration and the resulting formula to price the swaptions coincides with the Black���s one. However, the two models are not compatible from a theoretical point. Therefore, we derive various analytical approximating formulae to price the swaptions in the LIBOR market model and we explain how to perform a Monte Carlo simulation. Finally, we present the calibration of the LIBOR market model to the markets of both caps and swaptions, together with various examples of application to the historical correlation matrix and the cascade calibration of the forward volatilities to the matrix of implied swaption volatilities provided by the market.

Investigation on laser shock peening capability by FE simulation

Laser shock peening is a technique similar to shot peening that imparts compressive residual stresses in materials for improving fatigue resistance. The ability to use a high energy laser pulse to generate shock waves, inducing a compressive residual stress field in metallic materials, has applications in multiple fields such as turbo-machinery, airframe structures, and medical appliances. The transient nature of the LSP phenomenon and the high rate of the laser's dynamic make real time in-situ measurement of laser/material interaction very challenging. For this reason and for the high cost of the experimental tests, reliable analytical methods for predicting detailed effects of LSP are needed to understand the potential of the process. Aim of this work has been the prediction of residual stress field after Laser Peening process by means of Finite Element Modeling. The work has been carried out in the Stress Methods department of Airbus Operations GmbH (Hamburg) and it includes investigation on compressive residual stresses induced by Laser Shock Peening, study on mesh sensitivity, optimization and tuning of the model by using physical and numerical parameters, validation of the model by comparing it with experimental results. The model has been realized with Abaqus/Explicit commercial software starting from considerations done on previous works. FE analyses are ���Mesh Sensitive���: by increasing the number of elements and by decreasing their size, the software is able to probe even the details of the real phenomenon. However, these details, could be only an amplification of real phenomenon. For this reason it was necessary to optimize the mesh elements' size and number. A new model has been created with a more fine mesh in the trough thickness direction because it is the most involved in the process deformations. This increment of the global number of elements has been paid with an "in plane" size reduction of the elements far from the peened area in order to avoid too high computational costs. Efficiency and stability of the analyses has been improved by using bulk viscosity coefficients, a merely numerical parameter available in Abaqus/Explicit. A plastic rate sensitivity study has been also carried out and a new set of Johnson Cook's model coefficient has been chosen. These investigations led to a more controllable and reliable model, valid even for more complex geometries. Moreover the study about the material properties highlighted a gap of the model about the simulation of the surface conditions. Modeling of the ablative layer employed during the real process has been used to fill this gap. In the real process ablative layer is a super thin sheet of pure aluminum stuck on the masterpiece. In the simulation it has been simply reproduced as a 100��m layer made by a material with a yield point of 10MPa. All those new settings has been applied to a set of analyses made with different geometry models to verify the robustness of the model. The calibration of the model with the experimental results was based on stress and displacement measurements carried out on the surface and in depth as well. The good correlation between the simulation and experimental tests results proved this model to be reliable.

Characterisation and calibration of optical counters for airborne particulate matter

Gli aerosol, sospensione colloidale in aria di particelle solide o liquide, sono parte integrante dell���atmosfera. Essi interagiscono con la radiazione solare influenzando il clima (effetto primario e secondario) e la visibilit�� atmosferica. Gli aerosol hanno effetti sulla salute umana con patologie degli apparati cardiovascolare e circolatorio. La presente tesi affronta alcuni aspetti critici dei contatori ottici di particelle (OPC), utilizzati per caratterizzare l���aerosol ambientale. Gli OPC si basano sullo scattering luminoso per fornire la concentrazione in numero e la distribuzione dimensionale degli aerosol in tempo reale. Gli obiettivi di questa tesi sono: 1)caratterizzare e migliorare le prestazioni di un OPC di nuova concezione (CompactOPC N1, Alphasense; in seguito COPC) rispetto a un OPC standard commerciale (Grimm 1.108; in seguito GRM); 2)realizzare un banco di prova per la calibrazione di un OPC utilizzato in camere bianche e ambienti sanitari (Laser Particle Sensor 3715-00, Kanomax; in seguito LPS). Per questa attivit�� ha mostrato interesse un���azienda locale (Pollution Clean Air Systems S.p.A.; Budrio, BO). Le prove sperimentali sono state effettuate con aerosol indoor e con particelle monodisperse di latex polistirene (PSL) di dimensioni differenti campionando in parallelo con i diversi OPC e su filtro per osservazioni al microscopio elettronico a scansione (SEM). In questo modo si �� ottenuto un valore assoluto di riferimento per la concentrazione di aerosol. I risultati ottenuti indicano un buon accordo tra le concentrazioni di particelle fornite dal GRM e quelle ottenute al SEM. Il lavoro ha inoltre permesso di migliorare le prestazioni del COPC modificando la versione di base. Inoltre, �� stata effettuata la calibrazione del LPS tramite il banco di prova realizzato nella tesi. Il lavoro sperimentale �� stato svolto presso il Laboratorio di Aerosol e Fisica delle Nubi dell���Istituto di Scienze dell���Atmosfera e del Clima (ISAC) del Consiglio Nazionale delle Ricerche (CNR) a Bologna.

Studio e implementazione di tecniche di Hand Eye Calibration di un Braccio Robotico

La tesi indaga il problema di calibrazione Hand Eye, ovvero la trasformazione geometrica fra i diversi sistemi di riferimento della camera e dell'attuatore del robot, presentando il problema ed analizzando le varie soluzioni proposte in letteratura. Viene infine presentata una implementazione realizzata in collaborazione con l'azienda SpecialVideo, implementata utilizzando l'algoritmo proposto da Konstantinos Daniilidis, il quale propone una formulazione del problema sfruttando l'utilizzo di quaternioni duali, risolvendo simultaneamente la parte rotatoria e traslatoria della trasformazione. Si conclude il lavoro con una analisi dell'efficacia del metodo implementato su dati simulati e proponendo eventuali estensioni, allo scopo di poter riutilizzare in futuro il lavoro svolto nel software aziendale, con dati reali e con diversi tipi di telecamere, principalmente camere lineari o laser.