Lévy Process-Driven Asymmetric Heteroscedastic Option Pricing Model and Empirical Analysis

Abstract EN

This paper describes the peak, fat tail, and skewness characteristics of asset price via a Lévy process.

It applies asymmetric GARCH model to depict asset price’s random volatility characteristics and builds a GARCH-Lévy option pricing model with random jump characteristics.

It also uses circular maximum likelihood estimation technology to improve the stability of model parameter estimation.

In order to test the model’s pricing results, we use Hong Kong Hang Seng Index (HSI) price data and its option data to carry out empirical studies.

Results prove that the pricing bias of EGARCH-Lévy model is lower than that of standard Heston-Nandi (HN) model in the financial industry.

For short-term, middle-term, and long-term European-style options, the pricing error of EGARCH-Lévy model is the lowest.