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.

Main characteristics of the emission from elliptical galaxies

Elliptical galaxies are one of the most characteristic objects we can find in the sky. In order to unveil their properties, such as their structure or chemical composition, one must study their spectral emission. In fact they seem to behave rather differently when observed with different eyes. This is because their light is mainly brought by two different components: optical radiation arises from its stars, while the X emission is primarly due to a halo of extremely hot gas in which ellipticals seem to be embedded. After a brief classification, the two main processes linked to these phenomena will be described, together with the informations we can collect thanks to them. Eventually, we will take a quick look at the other regions of the electromagnetic spectrum.