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.

Multivariate analysis methods in the search for the Higgs boson produced in association with top pairs at the ATLAS experiment at LHC.

The Large Hadron Collider, located at the CERN laboratories in Geneva, is the largest particle accelerator in the world. One of the main research fields at LHC is the study of the Higgs boson, the latest particle discovered at the ATLAS and CMS experiments. Due to the small production cross section for the Higgs boson, only a substantial statistics can offer the chance to study this particle properties. In order to perform these searches it is desirable to avoid the contamination of the signal signature by the number and variety of the background processes produced in pp collisions at LHC. Much account assumes the study of multivariate methods which, compared to the standard cut-based analysis, can enhance the signal selection of a Higgs boson produced in association with a top quark pair through a dileptonic final state (ttH channel). The statistics collected up to 2012 is not sufficient to supply a significant number of ttH events; however, the methods applied in this thesis will provide a powerful tool for the increasing statistics that will be collected during the next LHC data taking.

Stochastic local volatility model for fx markets

Questa tesi verte sullo studio di un modello a volatilità stocastica e locale, utilizzato per valutare opzioni esotiche nei mercati dei cambio. La difficoltà nell'implementare un modello di tal tipo risiede nella calibrazione della leverage surface e uno degli scopi principali di questo lavoro è quello di mostrarne la procedura.

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).

Multivariate analysis to discriminate top quark pair production channels at LHC

Il quark top è una delle particelle fondamentali del Modello Standard, ed è osservato a LHC nelle collisioni a più elevata energia. In particolare, la coppia top-antitop (tt̄) è prodotta tramite interazione forte da eventi gluone-gluone (gg) oppure collisioni di quark e antiquark (qq̄). I diversi meccanismi di produzione portano ad avere coppie con proprietà diverse: un esempio è lo stato di spin di tt̄, che vicino alla soglia di produzione è maggiormente correlato nel caso di un evento gg. Uno studio che voglia misurare l’entità di tali correlazioni risulta quindi essere significativamente facilitato da un metodo di discriminazione delle coppie risultanti sulla base del loro canale di produzione. Il lavoro qui presentato ha quindi lo scopo di ottenere uno strumento per effettuare tale differenziazione, attraverso l’uso di tecniche di analisi multivariata. Tali metodi sono spesso applicati per separare un segnale da un fondo che ostacola l’analisi, in questo caso rispettivamente gli eventi gg e qq̄. Si dice che si ha a che fare con un problema di classificazione. Si è quindi studiata la prestazione di diversi algoritmi di analisi, prendendo in esame le distribuzioni di numerose variabili associate al processo di produzione di coppie tt̄. Si è poi selezionato il migliore in base all’efficienza di riconoscimento degli eventi di segnale e alla reiezione degli eventi di fondo. Per questo elaborato l’algoritmo più performante è il Boosted Decision Trees, che permette di ottenere da un campione con purezza iniziale 0.81 una purezza finale di 0.92, al costo di un’efficienza ridotta a 0.74.