Gatheral double stochastic volatility model with Skorokhod reflection
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915287146692608 |
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| author | Mishura, Yuliya Pilipenko, Andrey Ralchenko, Kostiantyn |
| author_facet | Mishura, Yuliya Pilipenko, Andrey Ralchenko, Kostiantyn |
| contents | We investigate the Gatheral model of double mean-reverting stochastic volatility, in which the drift term itself follows a mean-reverting process, and the overall model exhibits mean-reverting behavior. We demonstrate that such processes can attain values arbitrarily close to zero and remain near zero for extended periods, making them practically and statistically indistinguishable from zero. To address this issue, we propose a modified model incorporating Skorokhod reflection, which preserves the model's flexibility while preventing volatility from approaching zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09184 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gatheral double stochastic volatility model with Skorokhod reflection Mishura, Yuliya Pilipenko, Andrey Ralchenko, Kostiantyn Mathematical Finance Probability Pricing of Securities 60H10, 91G30, 91G80 We investigate the Gatheral model of double mean-reverting stochastic volatility, in which the drift term itself follows a mean-reverting process, and the overall model exhibits mean-reverting behavior. We demonstrate that such processes can attain values arbitrarily close to zero and remain near zero for extended periods, making them practically and statistically indistinguishable from zero. To address this issue, we propose a modified model incorporating Skorokhod reflection, which preserves the model's flexibility while preventing volatility from approaching zero. |
| title | Gatheral double stochastic volatility model with Skorokhod reflection |
| topic | Mathematical Finance Probability Pricing of Securities 60H10, 91G30, 91G80 |
| url | https://arxiv.org/abs/2505.09184 |