Numerical analysis on locally risk-minimizing strategies for Barndorff-Nielsen and Shephard models
Abstract
We develop a numerical method for locally risk-minimizing (LRM) strategies for Barndorff-Nielsen and Shephard (BNS) models. Arai et al. (2017) derived a mathematical expression for LRM strategies in BNS models using Malliavin calculus for L\'evy processes and presented some numerical results only for the case where the asset price process is a martingale. Subsequently, Arai and Imai (2024) developed the first Monte Carlo (MC) method available for non-martingale BNS models with infinite active jumps. Here, we modify the expression obtained by Arai et al. (2017) into a numerically tractable form, and, using the MC method developed by Arai and Imai (2024), propose a numerical method of LRM strategies available for non-martingale BNS models with infinite active jumps. In the final part of this paper, we will conduct some numerical experiments.
Keywords
Cite
@article{arxiv.2505.00255,
title = {Numerical analysis on locally risk-minimizing strategies for Barndorff-Nielsen and Shephard models},
author = {Takuji Arai},
journal= {arXiv preprint arXiv:2505.00255},
year = {2025}
}
Comments
16 pages, 2 figures