Explicit positivity preserving numerical method for linear stochastic volatility models driven by $α$-stable process
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909472901824512 |
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| author | Li, Xiaotong Liu, Wei Mao, Xuerong Tian, Hongjiong Wu, Yue |
| author_facet | Li, Xiaotong Liu, Wei Mao, Xuerong Tian, Hongjiong Wu, Yue |
| contents | In this paper, we introduce a linear stochastic volatility model driven by $α$-stable processes, which admits a unique positive solution. To preserve positivity, we modify the classical forward Euler-Maruyama scheme and analyze its numerical properties. The scheme achieves a strong convergence order of $1/α$. Numerical simulations are presented at the end to verify theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00788 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explicit positivity preserving numerical method for linear stochastic volatility models driven by $α$-stable process Li, Xiaotong Liu, Wei Mao, Xuerong Tian, Hongjiong Wu, Yue Probability 60H35, 65C30, 60J76 In this paper, we introduce a linear stochastic volatility model driven by $α$-stable processes, which admits a unique positive solution. To preserve positivity, we modify the classical forward Euler-Maruyama scheme and analyze its numerical properties. The scheme achieves a strong convergence order of $1/α$. Numerical simulations are presented at the end to verify theoretical results. |
| title | Explicit positivity preserving numerical method for linear stochastic volatility models driven by $α$-stable process |
| topic | Probability 60H35, 65C30, 60J76 |
| url | https://arxiv.org/abs/2502.00788 |