Application of Normal Inverse Gaussian Process in European Option Pricing

DOI: https://doi.org/10.62517/jse.202511603

Author(s)

He Jiancong

Affiliation(s)

China International Capital Corporation Beijing, Beijing, China

Abstract

The traditional Black-Scholes (BS) model, based on the geometric Brownian motion assumption, struggles to account for the fat-tail, spike, and volatility time-varying characteristics of asset prices in financial markets, leading to pricing deviations in options. This paper introduces the Normal Inverse Gaussian (NIG) process into European option pricing research, verifying its applicability through theoretical derivations and empirical analysis. First, we review the core theories of Levy process, inverse Gaussian process, and NIG process, deriving the European option pricing formula under NIG. Second, using daily data from 5 U.S. listed companies and 3 global stock indices, we compare the fitting performance of NIG distribution with normal distribution. Finally, employing Monte Carlo simulation, we calculate S&P 500 European call option prices using both NIG and BS models, evaluating pricing accuracy through Mean Absolute Error Rate (MAER). Empirical results demonstrate that NIG distribution effectively captures the fat-tail characteristics of financial data, yielding pricing results closer to actual market prices with significantly lower MAER than BS models, providing a superior methodological choice for European option pricing.

Keywords

Normal Inverse Gaussian Process; European Option Pricing; Black-Scholes Model

References

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