A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions

TLDR

The COS method exploits the close relationship between the characteristic function and the Fourier‑cosine series coefficients of the density function. The authors introduce the COS method for pricing European options and outline its application in this paper, with a follow‑up study on early‑exercise options. The COS method applies a Fourier‑cosine series expansion to the characteristic function, enabling efficient pricing for any asset process with a known characteristic function and various option types. The COS method converges exponentially and runs in linear computational time in most cases.

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 computational complexity is linear. Its range of application covers underlying asset processes for which the characteristic function is known and 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 with European options in particular. In a follow-up paper we will present its application to options with early-exercise features.