Quantiles of Lévy processes and applications in finance

This paper provides a survey of results on the quantiles of a Brownian motion with drift as well as a general Lévy process. The motivation is to calculate the price of related financial options. At the end of the paper some new results on variability orderings between various quantities associated with path dependent and European options are presented. This survey is not exhaustive, but intends to provide a flavour of research carried out in the area.