Approximation of Distribution of Log-returns with Normal Inverse Gaussian Process

Abstract

Normal inverse Gaussian (NIG) distribution is a quit a new distribution introduced in 1997. This is distribution, which describes evolution of NIG process. It appears that in many cases NIG distribution describes log-returns of stock prices with a high accuracy. Unlike normal distribution, it has higher kurtosis, which is necessary to fit many historical returns. This gives the opportunity to construct precise algorithms for hedging risks of options. The aim of this work is to evaluate how good NIG distribution can reproduce stock price dynamics and to illuminate future fields of applications.