Metodi perturbativi per E.D.P e applicazioni in finanza matematica

In questa tesi si discute di alcuni modelli di pricing per opzioni di tipo europeo e di opportuni metodi perturbativi che permettono di trovare approssimazioni soddisfacenti dei prezzi e delle volatilità implicite relative a questi modelli.

Alimenti Funzionali e Componenti Nutraceutici come Biomodulatori

Recent knowledge supports the hypothesis that, beyond meeting nutrition needs, diet may modulate various functions in the body and play beneficial roles in some diseases. Research on functional foods is addressing the physiologic effects and health benefits of foods and food components, with the aim of authorizing specific health claims. The recognition that oxidative stress plays a major role in the pathophysiology of cardiac disorders has led to extensive investigations of the protective effects of exogenous antioxidants, but results are controversial. A promising strategy for protecting cardiac cells against oxidative damage may be through the induction of endogenous phase 2 enzymes with the enhancement of cellular antioxidant capacity. Sulforaphane (SF), a naturally occurring isothiocyanate abundant in Cruciferous vegetables, has gained attention as a potential chemopreventive compound thanks to its ability to induce several classes of genes implicated in reactive oxygen species (ROS) and electrophiles detoxification. Antioxidant responsive element (ARE)-mediated gene induction is a pivotal mechanism of cellular defence against the toxicity of electrophiles and ROS. The transcription factor NF-E2-related factor-2 (Nrf2), is essential for the up-regulation of these genes. We investigated whether SF could exert cardioprotective effects against oxidative stress and elucidated the mechanisms underpinning these effects. Accordingly, using cultured rat neonatal cardiomyocytes as a model system, we evaluated the time-dependent induction of gene transcription, the corresponding protein expression and activity of various antioxidant and phase 2 enzymes (catalase, superoxide dismutase, glutathione and related enzymes glutathione reductase, glutathione peroxidase and glutathione S-transferase, NAD(P)H: quinone oxidoreductase 1 and thioredoxine reductase) elicited by SF. The results were correlated to intracellular ROS production and cell viability after oxidative stress generated by H2O2, and confirmed the ability of SF to exert cytoprotective effects acting as an indirect antioxidant. Furthermore, to get better insight into SF mechanism of action, we investigated the effect of SF treatment on Nrf2 and the upstream signalling pathways MAPK ERK1/2 and PI3K/Akt, known to mediate a pro survival signal in the heart. The use of specific inhibitors of ERK1/2 and Akt phosphorylation demonstrated their involvement in phase 2 enzymes induction. The concentration of SF tested in this study is comparable to peak plasma concentration achieved after dietary exposure giving clear relevance to our data to support dietary intake of Cruciferous vegetables in cytoprotection against oxidative stress, a common determinant of many cardiovascular diseases.

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.

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.

Sulla Frontiera Libera del Problema con Ostacolo per l'Opzione Put Americana

In questa tesi vengono presentate le prime semplici proprietà della Frontiera Libera relativa alla soluzione del Problema con Ostacolo per l'Operatore di Black & Scholes nel caso dell'Opzione Put Americana. Si ricavano inoltre le cosiddette Equazioni Integrali per la Frontiera Libera, ossia un sistema di equazioni in forma integrale che caratterizzano completamente tale insieme.

Disponibilità degli effetti della risoluzione e reviviscenza del contratto

La ricerca sul tema “Disponibilità degli effetti della risoluzione e reviviscenza del contratto” analizza se, e come, gli effetti della risoluzione possano essere oggetto di disposizione ad opera delle parti. In particolare, se, ed in che modo, il contraente non inadempiente che abbia agito in risoluzione, in via giudiziale o stragiudiziale, possa incidere unilateralmente sulla sorte finale del vincolo contrattuale paralizzando l’effetto risolutivo già in atto attraverso una tardiva richiesta di adempimento. La questione della reversibilità dell’effetto risolutivo, che si è posta in forma paradigmatica nell’ambito della diffida ad adempiere, ha diviso dottrina e giurisprudenza per oltre trent’anni: laddove la giurisprudenza ha costantemente ammesso il creditore a recuperare il contratto risolto e a pretenderne ancora l’esecuzione, ritenendo che la risoluzione concreti un vantaggio unilaterale del creditore, da lui sempre liberamente disponibile, la dottrina ha optato per la irreversibilità dell’effetto risolutivo, in ossequio al principio di tutela dell’affidamento dell’inadempiente ad aver certezza sulla sorte finale del vincolo e a non rimanere esposto a tempo indefinito agli arbitri di controparte. Sono di recente intervenute le Sezioni Unite (Cass., sez. un., 14 gennaio 2009, n. 553), che, in direzione diametralmente opposta rispetto al granitico orientamento giurisprudenziale, hanno integralmente accolto i rilievi critici della dottrina ed escluso la disponibilità dell’effetto risolutivo derivante dallo spirare inutile del termine fissato in diffida, con ciò precludendo al contraente non inadempiente di tornare a esigere l’adempimento a risoluzione avvenuta.