Infinite variance distributions are among the competing models used to explain the non-normality of stock price changes (Mandelbrot, 1963; Fama, 1965; Mandelbrot and Taylor, 1967; Rachev and Samorodnitsky, 1993). We investigate the asymptotic option price formula in infinite variance setting for both independent and correlated data using point processes. As we shall see the application of point process models can also leads us to establish a more general option price formula.

Spectral analysis can be used to identify and to quantify the different frequency components of a data series. Filters permit to capture speci…fic components (e.g. trends, cycles, seasonalities) of the original time-series. Both spectral analysis and standard fi…ltering methods have two main drawbacks: (i) they impose strong restrictions regarding the possible processes underlying the dynamics of the series (e.g. stationarity), and, (ii) they lead to a pure frequency-domain representation of the data, i.e.

In this project we used recent advances in heavy tailed distributions and jump processes to make a survey about new developments in  Portfolio Optimization and Capital Asset Pricing Models.