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.

Experimental analysis of fiber reinforced cementitious matrix (FRCM) confined masonry columns

The increasing use of Fiber Reinforced methods for strengthening existing brick masonry walls and columns, especially for the rehabilitation of historical buildings, has generated considerable research interest in understanding the failure mechanism in such systems. This dissertation is aimed to provide a basic understanding of the behavior of solid brick masonry walls unwrapped and wrapped with Fiber Reinforced Cementitious Matrix Composites. This is a new type of composite material, commonly known as FRCM, featuring a cementitious inorganic matrix (binder) instead of the more common epoxy one. The influence of the FRCM-reinforcement on the load-carrying capacity and strain distribution during compression test will be investigated using a full-field optical technique known as Digital Image Correlation. Compression test were carried on 6 clay bricks columns and on 7 clay brick walls in three different configuration, casted using bricks scaled respect the first one with a ratio 1:2, in order to determinate the effects of FRCM reinforcement. The goal of the experimental program is to understand how the behavior of brick masonry will be improved by the FRCM-wrapping. The results indicate that there is an arching action zone represented in the form of a parabola with a varying shape according to the used configuration. The area under the parabolas is considered as ineffectively confined. The effectively confined area is assumed to occur within the region where the arching action had been fully developed.