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.

Addizione di Michael organocatalitica asimmetrica di composti 1,3-dicarbonilici ad orto-chinoni metidi: un nuovo e semplice approccio alla preparazione di 4H-cromeni e croman-2-oni otticamente attivi

The work described in this thesis deals with the development of the asymmetric organocatalytic conjugate addition reaction of 1,3-dicarbonyl compounds to ortho-quinone methides. Due to their instability, these synthetically appealing intermediates have not been fully exploited in catalytic asymmetric settings. In this work, the instability of ortho-quinone methides is overcome by their generation in situ under mild basic conditions, starting from the corresponding sulfonyl derivatives. The bifunctional catalysts used are able to activate both substrates for the reaction, by means of a synergic action of the two catalytic sites, inducing at the same time high enantioselection in the addition step. The reaction leads to the generation of a 2-alkylphenolic framework, featuring a chiral centre at the benzylic position. In particular, the employment of acetylacetone and Meldrum acid as nucleophiles has allowed the obtainment of 4H-chromenes and chroman-2-ones in good yields and generally excellent enantioselectivities. These compounds are synthetic precursors of several natural products, some of which showing interesting biological activity, and of some active pharmaceutical ingredients used in commercial drugs.

Microchannel heat exchangers: An attractive option for the regenerator of a mobile orc waste heat recovery system

The performance of microchannel heat exchangers was assessed in gas-to-liquid applications in the order of several tens of kWth . The technology is suitable for exhaust heat recovery systems based on organic Rankine cycle. In order to design a light and compact microchannel heat exchanger, an optimization process is developed. The model employed in the procedure is validated through computational fluid-dynamics analysis with commercial software. It is shown that conjugate effects have a significant impact on the heat transfer performance of the device.

Regularization methods for the solution of a nonlinear least-squares problem in tomography

In this work we study a polyenergetic and multimaterial model for the breast image reconstruction in Digital Tomosynthesis, taking into consideration the variety of the materials forming the object and the polyenergetic nature of the X-rays beam. The modelling of the problem leads to the resolution of a high-dimensional nonlinear least-squares problem that, due to its nature of inverse ill-posed problem, needs some kind of regularization. We test two main classes of methods: the Levenberg-Marquardt method (together with the Conjugate Gradient method for the computation of the descent direction) and two limited-memory BFGS-like methods (L-BFGS). We perform some experiments for different values of the regularization parameter (constant or varying at each iteration), tolerances and stop conditions. Finally, we analyse the performance of the several methods comparing relative errors, iterations number, times and the qualities of the reconstructed images.