Modelli stocastici per tassi di trasferimento e di interesse

Questa tesi nasce come risultato di un'esperienza di stage svolta presso l'ufficio Pianificazione e Risk Management in Cassa di Risparmio di Cento; l'obiettivo di questo lavoro è la descrizione dell'analisi da me svolta per la ricostruzione del metodo di determinazione del tasso interno di trasferimento adottato in questa banca. A questo studio è stata aggiunta una sezione legata all'analisi e all'implementazione di due modelli stocastici per l'evoluzione dei tassi di interesse (modello di Vasicek e modello CIR).

Dupire's formula for exponential Lévy models

Questa tesi è incentrata sull'analisi della formula di Dupire, che permette di ottenere un'espressione della volatilità locale, nei modelli di Lévy esponenziali. Vengono studiati i modelli di mercato Merton, Kou e Variance Gamma dimostrando che quando si è off the money la volatilità locale tende ad infinito per il tempo di maturità delle opzioni che tende a zero. In particolare viene proposta una procedura di regolarizzazione tale per cui il processo di volatilità locale di Dupire ricrea i corretti prezzi delle opzioni anche quando si ha la presenza di salti. Infine tale risultato viene provato numericamente risolvendo il problema di Cauchy per i prezzi delle opzioni.

Mimicking the one-dimensional marginal distributions of stochastic diffusions

In the large maturity limit, we compute explicitly the Local Volatility surface for Heston, through Dupire’s formula, with Fourier pricing of the respective derivatives of the call price. Than we verify that the prices of European call options produced by the Heston model, concide with those given by the local volatility model where the Local Volatility is computed as said above.

Forward implied volatility expansions in LSV models

In this work we address the problem of finding formulas for efficient and reliable analytical approximation for the calculation of forward implied volatility in LSV models, a problem which is reduced to the calculation of option prices as an expansion of the price of the same financial asset in a Black-Scholes dynamic. Our approach involves an expansion of the differential operator, whose solution represents the price in local stochastic volatility dynamics. Further calculations then allow to obtain an expansion of the implied volatility without the aid of any special function or expensive from the computational point of view, in order to obtain explicit formulas fast to calculate but also as accurate as possible.

Disuguaglianza puntuale di Doob

In questa tesi si dimostra la disuguaglianza puntuale di Doob e si spiega perché è importante nell'ambito della finanza matematica

Study of molecular mechanisms in cardio- and neuroprotection and possibility of modulation by nutraceutical phytocomponents

Ischemic preconditioning is a complex cardioprotective phenomenon that involves adaptive changes in cells and molecules. This adaptation occurs in a biphasic pattern: an early phase which develops after 1-2 h, and a late phase that develops after 12-24 h. While it is widely accepted that reactive oxygen species (ROS) are strongly involved in triggering ischemic preconditiong, it is not clear if they play a major role in the early or late phase of preconditioning and which are the mechanisms involved. Methylglyoxal, a metabolic compound formed mainly from the glycolytic intermediate glyceraldehyde-3-phosphate., is a precursor of advanced glycation end product (AGEs) .It is more reactive than glucose and shows a stronger ability to cross-link with protein amino groups to form AGEs. Methylglyoxal induced cytotoxicity may be at least partially responsible for cardiovascular and Alzheimer diseases. Methylglyoxal omeostasis is controlled by the glyoxalase system that consists of two enzyme, glyoxalase 1 (GLO1) and glyoxalase 2. In a recent study it was demonstrated that the transcriptional levels of GLO1 are controlled by NF-E2-related factor 2 (Nrf2). The isothiocyanate sulforaphane, derived from the hydrolysis of glucoraphanin abundantly present in broccoli, represents one of the most potent inducers of phase II enzymes through the Keap1–Nrf2 pathway. The aim of this thesis was evaluated molecular mechanisms in cardio- and neuroprotection and the possibility of modulation by nutraceutical phytocomponents This thesis show to one side that the protection induced by H2O2 is mediated by detoxifying and antioxidant phase II enzymes induction, regulated, not only by transcriptional factor Nrf2, but also by Nrf1; on the other side our data represent an innovative result because for the first time it was demonstrated the possibility of inducing GLO1 by SF supplementation.

Diversity of microbial communities at shallow-hydrothermal vents off Dominica, Lesser Antilles

Hydrothermal vents are often compared to desert oases, because of the presence of highly diverse and abundant biotic communities inhabiting these extreme environments. Nevertheless, the microbial communities associated with shallow-hydrothermal systems have been poorly studied. Hydrothermal activity at Dominica Island is quite well known under the geological and geochemical aspects, but no previous information existed about the microbial communities associated to this area. This thesis is therefore targeting the microbiology of hydrothermal sediments combining geochemical and molecular biological investigations, focusing on differences between hydrothermal vents and background (i.e. control) areas, and between hydrothermal sites. It was also intended to assess relationship between geochemical parameters and microbial diversity at the two hydrothermally impacted sites. Two shallow-sea hydrothermal vents located south-west off Dominica Island (Lesser Antilles) have been investigated in this study: Champagne Hot Springs and Soufriere Bay offshore vent. During this study, sediments for geochemical and molecular analyses were collected every 2 cm from the two impacted areas and from two control sites not associated with hydrothermal activity; in situ temperatures measurements were also taken every 5 cm deep in the sediment for all the sites. A geochemical characterization of the sediment porewater was performed through the analysis of several elements’ concentrations (i.e. H2S, Cl-, Br-, SO42-, Fe2+, Na+, K+, B+, Si+). Microbial communities at the different sites were studied by Automated Intergenic Spacer Analysis (ARISA). Inspection of the operational taxonomic units (OTUs) distribution was performed, as well as statistical analyses for communities’ structure and composition differences, and for changes of β-diversity along with sediment geochemistry. Data suggested that mixing between hydrothermal fluids and seawater results in distinct different environmental gradients and potential ecological niches between the two investigated hydrothermal vents, reflecting a difference in microbial community structures between them.

Metodi di approssimazione saddlepoint ed applicazioni finanziarie

I metodi saddlepoint studiati nella tesi permettono di approssimare la densità di una variabile aleatoria a partire dalla funzione generatrice dei cumulanti (ricavabile dalla funzione caratteristica). Integrando la densità saddlepoint si ottiene la formula di Lugannani-Rice (e ulteriori generalizzazioni) per approssimare le probabilità di coda. Quest'ultima formula è stata poi applicata in ambito finanziario per il calcolo del prezzo di un'opzione call rispetto a vari modelli (Black-Scholes, Merton, CGMY)e in ambito assicurativo per calcolare la probabilità che il costo totale dei sinistri in una polizza non superi una certa quota fissata.

Statistical arbitrage on commodities

Questa tesi è incentrata sull'analisi dell'arbitraggio statistico, strategia di trading che cerca di trarre profitto dalle fluttuazioni statistiche di prezzo di uno o più asset sulla base del loro valore atteso. In generale, si creano opportunità di arbitraggio statistico quando si riescono ad individuare delle componenti sistematiche nelle dinamiche dei prezzi di alcuni asset che si muovono con regolarità persistenti e prevalenti. Perturbazioni casuali della domanda e dell’offerta nei mercati possono causare divergenze nei prezzi, dando luogo a opportunità di intermarket spread, ossia simultanei acquisto e vendita di commodities correlate tra loro. Vengono approfonditi vari test econometrici, i test unit root utilizzati per verificare se una serie storica possa essere modellizzata con un processo random walk. Infine viene costruita una strategia di trading basata sull'arbitraggio statistico e applicata numericamente alle serie storiche dal 2010 al 2014 di due titoli azionari sul petrolio: Brent e WTI.

Il teorema di Carathéodory

teorema di estensione di Carathéodory

Replicazione di opzioni con costi di transazione

Replicazione di un'opzione call europea con costi di transazione proporzionali alla quantità di stock scambiata, in tempi discreti.

Pricing in stochastic-local volatility models with default

In recent years is becoming increasingly important to handle credit risk. Credit risk is the risk associated with the possibility of bankruptcy. More precisely, if a derivative provides for a payment at cert time T but before that time the counterparty defaults, at maturity the payment cannot be effectively performed, so the owner of the contract loses it entirely or a part of it. It means that the payoff of the derivative, and consequently its price, depends on the underlying of the basic derivative and on the risk of bankruptcy of the counterparty. To value and to hedge credit risk in a consistent way, one needs to develop a quantitative model. We have studied analytical approximation formulas and numerical methods such as Monte Carlo method in order to calculate the price of a bond. We have illustrated how to obtain fast and accurate pricing approximations by expanding the drift and diffusion as a Taylor series and we have compared the second and third order approximation of the Bond and Call price with an accurate Monte Carlo simulation. We have analysed JDCEV model with constant or stochastic interest rate. We have provided numerical examples that illustrate the effectiveness and versatility of our methods. We have used Wolfram Mathematica and Matlab.

Modello di Hull-White discreto

In questa tesi è stato trattato il tema dei derivati sui tassi di interesse e approfondito il modello stocastico discreto di Hull-White.

Involvement of microRNAs in Androgen Receptor-dependent Breast Cancers

Triple negative breast cancer (TNBC) is a very aggressive tumor subtype characterized by the lack of expression of estrogen receptor 1 (ESR1), due in the most of cases to an increased expression of DNA methyltransferases (DNMTs) and hypermethylation in CpG islands, resulting in gene silencing. Furthermore, in ESR1- negative breast cancers, androgen receptor (AR) is highly expressed and some studies suggest that it can drive tumor progression and might represent a therapeutic target. A correlation between microRNAs, small non-coding RNAs that regulate gene expression, and DNMTs was investigated in a TNBC cell line to restore a normal methylation pattern of ESR1, leading to its re-expression and conferring again sensitivity to selective estrogen receptor modulators (SERMs). miR-148A and miR-29B were found to be involved in the reduction of the expression of DNMT1 and DNMT3A and in a slight increase of ESR1 expression, but not at protein level. Then, we found a down-regulation of AR by miRs-7, -9, -27a, -27b, -29a, -29b, -29c, -127-3p, -127-5p and -376 at 48h post transfection and an up-regulation by miR-15a and miR-16 at every time considered. We concomitantly investigated a possible increase of Tamoxifen, Herceptin and Metformin sensitivity after AR silencing in MDA-MB 453 and T-47D cell lines. Cells seemed more sensitive when silenced for AR only in MDA-MB-453 at 24h post Tamoxifen treatment. Studies on Metformin have basically confirmed an increase of drug sensitivity due to AR silencing in both cell lines. Analysis of Herceptin showed how MDA-MB 453 samples silenced for AR have a slight decrease in the percentage of proliferating cells, demonstrating a possible increase in the response to treatment. These preliminary data provide the basis for further study of the modulation of the expression of AR by microRNAs and it will be interesting to understand the molecular mechanisms underlying these interactions.

Role of Reactive Oxygen Species in signalling and oxidative stress

Results reported in this Thesis contribute to the comprehension of the complicated world of “redox biology”. ROS regulate signalling pathways both in physiological responses and in pathogenesis and progression of diseases. In cancer cells, the increase in ROS generation from metabolic abnormalities and oncogenic signalling may trigger a redox adaptation response, leading to an up-regulation of antioxidant capacity in order to maintain the ROS level below the toxic threshold. Thus, cancer cells would be more dependent on the antioxidant system and more vulnerable to further oxidative stress induced by exogenous ROS-generating agents or compounds that inhibit the antioxidant system. Results here reported indicate that the development of new drugs targeting specific Nox isoforms, responsible for intracellular ROS generation, or AQP isoforms, involved in the transport of extracellular H2O2 toward intracellular targets, might be an interesting novel anti-leukaemia strategy. Furthermore, also the use of CSD peptide, which simulate the VEGFR-2 segregation into caveolae in the inactive form, might be a strategy to stop the cellular response to VEGF signalling. As above stated, in the understanding of the redox biology, it is also important to identify and distinguish the molecular effectors that maintain normal biological and physiological responses, such as agents that stimulate our adaptation systems and elevate our endogenous antioxidant defences or other protective systems. Data here reported indicate that the nutraceutical compound sulforaphane and the Klotho protein are able to stimulate the HO-1 and Prx-1 expression, as well as the GSH levels, confirming their antioxidant and protective role. Finally, results here reported demonstrated that Stevia extracts are involved in insulin regulated glucose metabolism, suggesting that the use of these compounds goes beyond their sweetening power and may also offer therapeutic benefits hence improving the quality of life.