On the difference between locally risk-minimizing and delta hedging strategies for exponential L\'evy models

TL;DR

This paper compares locally risk-minimizing and delta hedging strategies in exponential Lévy models, providing upper bounds and numerical examples for Merton and variance gamma models.

Contribution

It offers the first model-independent bounds on the difference between these hedging strategies and demonstrates their practical differences through numerical simulations.

Findings

Upper bounds for the difference between strategies

Numerical comparisons for Merton and variance gamma models

Insights into the effectiveness of delta hedging in Lévy models

Abstract

We discuss the difference between locally risk-minimizing and delta hedging strategies for exponential L\'evy models, where delta hedging strategies in this paper are defined under the minimal martingale measure. We give firstly model-independent upper estimations for the difference. In addition we show numerical examples for two typical exponential L\'evy models: Merton models and variance gamma models.