Pricing European Options by Stable Fourier-Cosine Series Expansions

TL;DR

This paper introduces a stable Fourier cosine series expansion method for pricing European call options, enhancing robustness and accuracy across various models like Heston, Kou, and CGMY.

Contribution

It develops a robust Fourier cosine series approach for option pricing, addressing stability issues present in previous methods.

Findings

The method demonstrates high accuracy in numerical examples.

It maintains stability across different stochastic models.

Error analysis confirms improved robustness.

Abstract

The COS method proposed in Fang and Oosterlee (2008), although highly efficient, may lack robustness for a number of cases. In this paper, we present a Stable pricing of call options based on Fourier cosine series expansion. The Stability of the pricing methods is demonstrated by error analysis, as well as by a series of numerical examples, including the Heston stochastic volatility model, Kou jump-diffusion model, and CGMY model.