Numerical analysis on quadratic hedging strategies for normal inverse Gaussian models

TL;DR

This paper develops numerical schemes for quadratic hedging strategies in models where asset prices follow an exponential normal inverse Gaussian process, providing practical tools for financial risk management.

Contribution

It introduces numerical methods for two key quadratic hedging strategies specifically tailored to NIG models, extending existing theoretical results to practical applications.

Findings

Numerical schemes successfully implemented for NIG models.

Results demonstrate effectiveness of hedging strategies in simulated scenarios.

Provides a foundation for further numerical analysis in Lévy process-based models.

Abstract

The authors aim to develop numerical schemes of the two representative quadratic hedging strategies: locally risk minimizing and mean-variance hedging strategies, for models whose asset price process is given by the exponential of a normal inverse Gaussian process, using the results of Arai et al. \cite{AIS}, and Arai and Imai. Here normal inverse Gaussian process is a framework of L\'evy processes frequently appeared in financial literature. In addition, some numerical results are also introduced.