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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2210.01214 |
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| _version_ | 1866909106523078656 |
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| author | Chong, Carsten Hoffmann, Marc Liu, Yanghui Rosenbaum, Mathieu Szymanski, Grégoire |
| author_facet | Chong, Carsten Hoffmann, Marc Liu, Yanghui Rosenbaum, Mathieu Szymanski, Grégoire |
| contents | Rough volatility models have gained considerable interest in the quantitative finance community in recent years. In this paradigm, the volatility of the asset price is driven by a fractional Brownian motion with a small value for the Hurst parameter $H$. In this work, we provide a rigorous statistical analysis of these models. To do so, we establish minimax lower bounds for parameter estimation and design procedures based on wavelets attaining them. We notably obtain an optimal speed of convergence of $n^{-1/(4H+2)}$ for estimating $H$ based on n sampled data, extending results known only for the easier case $H>1/2$ so far. We therefore establish that the parameters of rough volatility models can be inferred with optimal accuracy in all regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_01214 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Statistical inference for rough volatility: Minimax Theory Chong, Carsten Hoffmann, Marc Liu, Yanghui Rosenbaum, Mathieu Szymanski, Grégoire Statistics Theory Statistical Finance Rough volatility models have gained considerable interest in the quantitative finance community in recent years. In this paradigm, the volatility of the asset price is driven by a fractional Brownian motion with a small value for the Hurst parameter $H$. In this work, we provide a rigorous statistical analysis of these models. To do so, we establish minimax lower bounds for parameter estimation and design procedures based on wavelets attaining them. We notably obtain an optimal speed of convergence of $n^{-1/(4H+2)}$ for estimating $H$ based on n sampled data, extending results known only for the easier case $H>1/2$ so far. We therefore establish that the parameters of rough volatility models can be inferred with optimal accuracy in all regimes. |
| title | Statistical inference for rough volatility: Minimax Theory |
| topic | Statistics Theory Statistical Finance |
| url | https://arxiv.org/abs/2210.01214 |