Tesi di LAUREA SPECIALISTICA Titolo A Calibration Method for HJM Models based on the Levenberg-Marquardt Optimization Algorithm Data 2010-12-20 Autore/i Beltrami, Luca Relatore Sgarra, C. Relatore Carrillo Menendez, S. Full text non disponibile Abstract This work presents a particular approach to the calibration procedure for Heath-Jarrow-Morton models. Are analyzed precisely payer swap options for which have been computed prices through Monte Carlo simulations of the HJM dynamics. Results are compared with prices obtained using a Black like formula focusing on qualitative aspects due to the characteristic of the framework. The main problem has been to specify the volatility structure for practical purpose. So that has been taken under consideration the Hull-White model to provide it. This leads to the creative and interesting part of the work, which is the calibration procedure of the parameters of the model. For this aim, using Matlab is originally implemented the Levenberg-Marquardt optimization algorithm which minimize iteratively the sum of the square of the difference between Black and HW prices, paying particular attention to the behavior of the Hull-White model. The variables considered are precise and the parameters encountered respect the usual range of values present in the literature, confirming the goodness of the approach. The first three chapters consist in a theoretical part necessary for a better comprehension of the following development. Are presented the basis of the interest rate theory, then the Heath-Jarrow-Morton framework and its characteristic, and thirdly a description of interest rate derivatives. In chapter four is calculated the volatility structure for HJM through a calibration process of HW parameters involving the implementation of the Levenberg-Marquardt algorithm. The fifth chapter deals with the pricing of a payer swap option within the HJM dynamics involving Monte Carlo simulation. Finally are presented possible developments and conclusions, while in the appendices is exposed the Matlab code.