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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2505.00255 |
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| _version_ | 1866918005730967552 |
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| author | Arai, Takuji |
| author_facet | Arai, Takuji |
| contents | 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 Lévy 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00255 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical analysis on locally risk-minimizing strategies for Barndorff-Nielsen and Shephard models Arai, Takuji Computational Finance 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 Lévy 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. |
| title | Numerical analysis on locally risk-minimizing strategies for Barndorff-Nielsen and Shephard models |
| topic | Computational Finance |
| url | https://arxiv.org/abs/2505.00255 |