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.