An Accurate and Stable FFT-based Method for Pricing Options under Exp-Levy Processes

An accurate and stable method for pricing European options in exp-Levy models is presented. The main idea of this new method is combining the quadrature technique and the Carr-Madan Fast Fourier Transform methods. The theoretical analysis shows that the overall complexity of this new method is still O(N log N) with N grid points as the fast Fourier transform methods. Numerical experiments for different exp-Levy processes also show that the numerical algorithm proposed by this new method has an accuracy and stability for the small strike prices K. That develops and improves the Carr-Madan method.