Numerical analysis on local risk-minimization forexponential L\'evy models

TL;DR

This paper presents a method to compute local risk minimization for call options in exponential Lévy models using Fourier transform techniques, with applications to Merton jump-diffusion and variance gamma models.

Contribution

It transforms the LRM representation into a Fourier-based form enabling efficient computation, extending previous work to practical models.

Findings

Efficient Fourier-based computation of LRM for exponential Lévy models.

Application to Merton jump-diffusion and variance gamma models.

Demonstration of the method's effectiveness in concrete financial models.

Abstract

We illustrate how to compute local risk minimization (LRM) of call options for exponential L\'evy models. We have previously obtained a representation of LRM for call options; here we transform it into a form that allows use of the fast Fourier transform method suggested by Carr & Madan. In particular, we consider Merton jump-diffusion models and variance gamma models as concrete applications.