The Cos Method for European Options in the Normal Inverse Gaussian Framework

Abstract

The goal of this project is to explore the application of the Fourier-cosine expansion (COS) method within the framework of the Normal Inverse Gaussian (NIG) distribution for pricing European options, the COS-NIG model. The COS method, recognized as a highly e - cient numerical tool, plays a pivotal role in the accurate pricing of European options. Our key insight lies in the close relationship between the characteristic function and the series coe cients derived from the Fourier-cosine expansion of the density function. Leveraging the known characteristic function of the NIG distribution, we develop a COS-NIG model for pricing of European options. The choice of the NIG distribution for modeling stock options is motivated by its ability to capture skewness and kurtosis, given the existence of higher moments, in contrast to the Gaussian distribution. Notably, the chosen distribution allows for a more accurate representation of the empirical density of log-returns. In our investigation, the COS-NIG model consistently surpasses the performance of the Black Scholes Model (BSM) especially for In the Money call options.