ABSTRACT
A number of authors have recently proposed the use of infinite activity pure jump Le´vy processes for the process describing the dynamics of the asset’s logarithmic price (Eberlein, Keller, and Prause [105], Barndorff-Nielsen and Shephard [26] and Madan, Carr, and Chang [175]). Further it is argued in Geman, Madan, and Yor [118] that such processes are the norm when it is recognized that time changes with martingale components describe price evolution. At an empirical level, Carr, Geman, Madan and Yor [54] present evidence supporting the view that in the presence of an infinite activity Le´vy process one may effectively dispense with a diffusion component.
