Numerical analysis on locally risk-minimizing strategies for Barndorff-Nielsen and Shephard models

In this paper, we develop a numerical method for locally risk-minimizing (LRM) strategies for Barndorf–Nielsen and Shephard (BNS) models. Arai et al. (2017). Local risk-minimization for Barndorff-Nielsen and Shephard models, Finance & Stochastics, 21, 551–592 derived a mathematical expression for LRM strategies in BNS models using Malliavin calculus for Lévy processes and presented some numerical results only for the case where the asset price process is a martingale. Subsequently, Arai and Imai (2024). Monte Carlo simulation for Barndorff-Nielsen and Shephard model under change of measure, Mathematics and Computers in Simulation, 218, 223–234 developed the first Monte Carlo (MC) method available for nonmartingale BNS models with infinite active jumps. Here, we modify the expression obtained by Arai et al. (2017). Local risk-minimization for Barndorff-Nielsen and Shephard models, Finance & Stochastics, 21, 551–592 into a numerically tractable form, and, using the MC method developed by Arai and Imai (2024). Monte Carlo simulation for Barndorff–Nielsen and Shephard model under change of measure, Mathematics and Computers in Simulation, 218, 223–234, propose a numerical method of LRM strategies available for nonmartingale BNS models with infinite active jumps. In the final part of this paper, we will conduct some numerical experiments.