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arXiv · 2505.00255

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

Takuji Arai
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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.

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Takuji Arai. 2025-05-01. Numerical analysis on locally risk-minimizing strategies for Barndorff-Nielsen and Shephard models. https://arxiv.org/abs/2505.00255

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