Long memory score-driven models as approximations for rough Ornstein-Uhlenbeck processes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911307631951872 |
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| author | Wu, Yinhao He, Ping |
| author_facet | Wu, Yinhao He, Ping |
| contents | This paper investigates the continuous-time limit of score-driven models with long memory. By extending score-driven models to incorporate infinite-lag structures with coefficients exhibiting heavy-tailed decay, we establish their weak convergence, under appropriate scaling, to fractional Ornstein-Uhlenbeck processes with Hurst parameter $H < 1/2$. When score-driven models are used to characterize the dynamics of volatility, they serve as discrete-time approximations for rough volatility. We present several examples, including EGARCH($\infty$) whose limits give rise to a new class of rough volatility models. Building on this framework, we carry out numerical simulations and option pricing analyses, offering new tools for rough volatility modeling and simulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09105 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Long memory score-driven models as approximations for rough Ornstein-Uhlenbeck processes Wu, Yinhao He, Ping Probability Mathematical Finance 60F17, 60G22, 62M10, 91B70 This paper investigates the continuous-time limit of score-driven models with long memory. By extending score-driven models to incorporate infinite-lag structures with coefficients exhibiting heavy-tailed decay, we establish their weak convergence, under appropriate scaling, to fractional Ornstein-Uhlenbeck processes with Hurst parameter $H < 1/2$. When score-driven models are used to characterize the dynamics of volatility, they serve as discrete-time approximations for rough volatility. We present several examples, including EGARCH($\infty$) whose limits give rise to a new class of rough volatility models. Building on this framework, we carry out numerical simulations and option pricing analyses, offering new tools for rough volatility modeling and simulation. |
| title | Long memory score-driven models as approximations for rough Ornstein-Uhlenbeck processes |
| topic | Probability Mathematical Finance 60F17, 60G22, 62M10, 91B70 |
| url | https://arxiv.org/abs/2509.09105 |