A novel pricing method for European options based on Fouriercosine series expansions

Abstract. Here we develop an option pricing method for European options based on the Fourier-cosine series, and call it the COS method. The key insight is in the close relation of the characteristic function with the series coefficients of the Fourier-cosine expansion of the density function. In most cases, the convergence rate of the COS method is exponential and the computa-tional complexity is linear. Its range of application covers different underlying dynamics, including Lévy processes and the Heston stochastic volatility model, and various types of option contracts. We will present the method and its applications in two separate parts. The first one is this pa-per, where we deal with European options in particular. In a follow-up paper we will present its application to options with early-exercise features. 1. Introduction. Efficien