Strong Solutions and Quantization-Based Numerical Schemes for a Class of Non-Markovian Volatility Models
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| Format: | Preprint |
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2025
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| _version_ | 1866918292211367936 |
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| author | Grasselli, Martino Pagès, Gilles |
| author_facet | Grasselli, Martino Pagès, Gilles |
| contents | We investigate a class of non-Markovian processes that hold particular relevance in the realm of mathematical finance. This family encompasses path-dependent volatility models, including those pioneered by [Platen and Rendek, 2018] and, more recently, by [Guyon and Lekeufack, 2023]. Our study unfolds in two principal phases. In the first phase, we introduce a functional quantization scheme based on an extended version of the Lamperti transformation that we propose to handle the presence of a memory term incorporated into the diffusion coefficient. In the second phase, we study the problem of existence and uniqueness of a strong solution for the SDEs related to the examples that motivate our study, in order to provide a theoretical basis to correctly apply the proposed numerical schemes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_00243 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strong Solutions and Quantization-Based Numerical Schemes for a Class of Non-Markovian Volatility Models Grasselli, Martino Pagès, Gilles Mathematical Finance 60F10, 91G99, 91B25 We investigate a class of non-Markovian processes that hold particular relevance in the realm of mathematical finance. This family encompasses path-dependent volatility models, including those pioneered by [Platen and Rendek, 2018] and, more recently, by [Guyon and Lekeufack, 2023]. Our study unfolds in two principal phases. In the first phase, we introduce a functional quantization scheme based on an extended version of the Lamperti transformation that we propose to handle the presence of a memory term incorporated into the diffusion coefficient. In the second phase, we study the problem of existence and uniqueness of a strong solution for the SDEs related to the examples that motivate our study, in order to provide a theoretical basis to correctly apply the proposed numerical schemes. |
| title | Strong Solutions and Quantization-Based Numerical Schemes for a Class of Non-Markovian Volatility Models |
| topic | Mathematical Finance 60F10, 91G99, 91B25 |
| url | https://arxiv.org/abs/2503.00243 |