Tesi di LAUREA SPECIALISTICA Titolo Pricing di opzioni asiatiche nell’ambito dei processi di Lévy: il ruolo della Fast Fourier Transform Data 2011-12-20 Autore/i Raimondi, Daria Relatore Marazzina, D. Full text non disponibile Abstract This work presents four recursive methods to price discretely monitored Asian options where the Fast Fourier Transform plays a key role. Whether with recursion on the density of logreturns ([B02] and [FM08]) or directly on the option price ([CK09] and [FMM09]), the FFT is the tool used to compute log-returns density starting from the characteristic function, under the hypothesis that the underlying evolves according to a generic Lévy process. Furthermore, in [B02] and [CK09], the FFT is also used at every step of the recursion, whereas in the other articles numerical integration is performed. The algorithms are implemented and compared in the framework of the Black & Scholes model and generalized to Lévy processes. The content is organized as follows: Chapter 1 is an introduction to derivatives and pricing of discrete sampled Asian options. Chapter 2 describes Benhamou and Fusai-Meucci methods, with recursions on log-return density. Chapter 3 presents Cerný-Kyriakou and Fusai-Marazzina-Marena algorithms, focusing on price recursion. Chapter 4 generalizes the underlying price process and the algorithms to Lévy processes. Chapter 5 presents numerical results and conclusions.