Path dependent option pricing under Lévy processes applied to Bermudan options

A model is developed that can price path dependent options when the underlying process is an exponential Lévy process with closed form conditional characteristic function. The model is an extension of a recent quadrature option pricing model so that it can be applied with the use of Fourier and Fast Fourier transforms. Thus the model possesses nice features of both Fourier and quadrature option pricing techniques since it can be applied for a very general set of underlying Lévy processes and can handle exotic path dependent features. The model is applied to European and Bermudan options for geometric Brownian motion, a jump-diffusion process, a variance gamma process and a normal inverse Gaussian process. However it must be noted that the model can also price other path dependent exotic options such as lookback and Asian options.