Pricing di opzioni barriera con monitoraggio discreto

In this work we present a method to price barrer options when discretely monitoring is considered. We assume an exponential Lévy model as underlying, the KoBoL. For options with short maturity we deal with the parabolic inverse Fourier transform (Para iFT) and we show that the results agree with the Carr and Madan method for European options. We show that the Para iFT is much more efficient than the Flat method, which is the Carr and Madan one. After pricing European options with short maturity, we use the backward induction to price discretely monitored barrier options for longer maturities. The method consists in a linear interpolation of the value of the option and a convolution with the Fourier transform of this approximation and the transaction probability at each step of the backward induction