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.

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.

Orthogonal gamma-based expansions for volatility option prices under jump-diffusion dynamics

In my work I derive closed-form pricing formulas for volatility based options by suitably approximating the volatility process risk-neutral density function. I exploit and adapt the idea, which stands behind popular techniques already employed in the context of equity options such as Edgeworth and Gram-Charlier expansions, of approximating the underlying process as a sum of some particular polynomials weighted by a kernel, which is typically a Gaussian distribution. I propose instead a Gamma kernel to adapt the methodology to the context of volatility options. VIX vanilla options closed-form pricing formulas are derived and their accuracy is tested for the Heston model (1993) as well as for the jump-diffusion SVJJ model proposed by Duffie et al. (2000).

FX modelling under collateralization

We present the market practice for interest rate yield curves construction and pricing interest rate derivatives. Then we give a brief description of the Vasicek and the Hull-White models, with an example of calibration to market data. We generalize the classical Black-Scholes-Merton pricing formulas, considering more general cases such as perfect or partial collateral, derivatives on a dividend paying asset subject to repo funding, and multiple currencies. Finally we derive generic pricing formulae for different combinations of cash flow and collateral currencies, and we apply the results to the pricing of FX swaps and CCS, and we discuss curve bootstrapping.

Development of a colorimetric indicator label for food oxidation based on hexanal detection

In this work, a colorimetric indicator for food oxidation based on the detection of hexanal in gas-phase, has been developed. In fact, in recent years, the food packaging industry has evolved towards new generation of packaging, like active and intelligent. According to literature (Pangloli P. et al. 2002), hexanal is the main product of a fatty acid oxidation: the linoleic acid. So, it was chosen to analyse two kinds of potato chips, fried in two different oils with high concentration of linoleic acid: olive oil and sunflower oil. Five different formulas were prepared and their colour change when exposed to hexanal in gas phase was evaluated. The formulas evaluations were first conducted on filter paper labels. The next step was to select the thickener to add to the formula, in order to coat a polypropylene film, more appropriate than the filter paper for a production at industrial scale. Three kinds of thickeners were tested: a cellulose derivative, an ethylene vinyl-alcohol and a polyvinyl alcohol. To obtain the final labels with the autoadhesive layer, the polypropylene film with the selected formula and thickener was coat with a water based adhesive. For both filter paper and polypropylene labels, with and without autoadhesive layer, the detection limit and the detection time were measured. For the selected formula on filter paper labels, the stability was evaluated, when conserved on the dark or on the light, in order to determine the storage time. Both potato chips samples, stocked at the same conditions, were analysed using an optimised Headspace-Solid Phase Microextraction-Gas Chromatography-Mass Spectrometry (HS-SPME-GC-MS) method, in order to determine the concentration of volatilized hexanal. With the aim to establish if the hexanal can be considered as an indicator of the end of potato chips shelf life, sensory evaluation was conducted each day of HS-SPME-GC-MS analysis.

Dalla Sintesi di Leganti Polimerici alla Realizzazione di Adesivi da Parquet

This final report is part of a research project by Kerakoll S.P.A aimed to the realization and optimization of hybrid adhesive for the parquet using hybrid polyurethane silanizated (STPU). Hybrid polymers belong to polyurethane polymers which undergo an hybridization process where the classic isocyanate groups are converted into a alkoxysilylether terminated chain. The aim of this thesis was to realize hybrid polymers with specific proprieties compared to the indexes wanted by the company; another goal of this project was to use this polymers STPU to realize adhesive for the parquet which should be competitive in the adhesive market. All activities were carried out in a chemistry laboratory with specific tools for the synthesis of polymers and characterization of the finals products. The study led to two prototypes; the second was obtained thanks to the use of the experimental design procedure known as DOE (Design Of Experiment), a recently acquired approach by the company, which allows the rationalization of the formulas and the creation of a database that can be extended and implemented indefinitely.