Efficient computation of european option prices and their sensitivities with the complex fourier series method

Highly accurate approximation pricing formulae and option Greeks are obtained for European-type options using a complex Fourier series. We assume that risky assets are driven by exponential Lévy processes and affine stochastic volatility models. We provide a succinct error analysis to demonstrate that we can achieve an exponential convergence rate in the pricing method in many cases as long as we choose the correct truncated computational interval. As a novel pricing method, we also numerically demonstrate that the complex Fourier series performs either favourably or comparably with existing techniques in numerical experiments.