Jarrow-Yildirim model for inflation: theory and applications

This thesis deals with inflation theory, focussing on the model of Jarrow & Yildirim, which is nowadays used when pricing inflation derivatives. After recalling main results about short and forward interest rate models, the dynamics of the main components of the market are derived. Then the most important inflation-indexed derivatives are explained (zero coupon swap, year-on-year, cap and floor), and their pricing proceeding is shown step by step. Calibration is explained and performed with a common method and an heuristic and non standard one. The model is enriched with credit risk, too, which allows to take into account the possibility of bankrupt of the counterparty of a contract. In this context, the general method of pricing is derived, with the introduction of defaultable zero-coupon bonds, and the Monte Carlo method is treated in detailed and used to price a concrete example of contract. Appendixes: A: martingale measures, Girsanov's theorem and the change of numeraire. B: some aspects of the theory of Stochastic Differential Equations; in particular, the solution for linear EDSs, and the Feynman-Kac Theorem, which shows the connection between EDSs and Partial Differential Equations. C: some useful results about normal distribution.

Study of the calibration method of pressure-velocity probes and its application in a field of progressive plane waves

This dissertation presents a calibration procedure for a pressure velocity probe. The dissertation is divided into four main chapters. The first chapter is divided into six main sections. In the firsts two, the wave equation in fluids and the velocity of sound in gases are calculated, the third section contains a general solution of the wave equation in the case of plane acoustic waves. Section four and five report the definition of the acoustic impedance and admittance, and the practical units the sound level is measured with, i.e. the decibel scale. Finally, the last section of the chapter is about the theory linked to the frequency analysis of a sound wave and includes the analysis of sound in bands and the discrete Fourier analysis, with the definition of some important functions. The second chapter describes different reference field calibration procedures that are used to calibrate the P-V probes, between them the progressive plane wave method, which is that has been used in this work. Finally, the last section of the chapter contains a description of the working principles of the two transducers that have been used, with a focus on the velocity one. The third chapter of the dissertation is devoted to the explanation of the calibration set up and the instruments used for the data acquisition and analysis. Since software routines were extremely important, this chapter includes a dedicated section on them and the proprietary routines most used are thoroughly explained. Finally, there is the description of the work that has been done, which is identified with three different phases, where the data acquired and the results obtained are presented. All the graphs and data reported were obtained through the Matlab® routine. As for the last chapter, it briefly presents all the work that has been done as well as an excursus on a new probe and on the way the procedure implemented in this dissertation could be applied in the case of a general field.