A novel option pricing method based on Fouriercosine series expansions, submitted

Here we develop an option pricing method for European options based on the Fourier-cosine series, and call it the COS method. The convergence rate of the COS method is exponential and the computational complexity is linear. It has a wide range of applicability for different underlying dynamics, including Lévy processes and Heston’s stochastic volatility model, and for various types of option contracts. We will present the method and its applications in two separate parts. The first one is this paper, where we deal in particular with European options. In a follow-up paper, part II, we will present its application to options with early-exercise features.