Closed-form solutions for VIX derivatives in a Legendre empirical model
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909617622089728 |
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| author | Wang, Ying-Li Xu, Cheng-Long He, Ping |
| author_facet | Wang, Ying-Li Xu, Cheng-Long He, Ping |
| contents | In this paper, we introduce a data-driven, single-parameter Markov diffusion model for the VIX. The volatility factor evolves in $(-1,1)$ with a uniform invariant distribution ensured by Legendre polynomials, mapped to the empirical distribution. We derive analytical series solutions for VIX futures and options using separation of variables to solve the Feynman-Kac PDE. Compared to the 3/2 model, our approach offers equal or superior accuracy and flexibility, providing an efficient, robust alternative for VIX pricing and risk management. Code and data are available at github.com/gagawjbytw/empirical-VIX. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_08175 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Closed-form solutions for VIX derivatives in a Legendre empirical model Wang, Ying-Li Xu, Cheng-Long He, Ping Pricing of Securities Risk Management 91G20, 60J25, 65C30 In this paper, we introduce a data-driven, single-parameter Markov diffusion model for the VIX. The volatility factor evolves in $(-1,1)$ with a uniform invariant distribution ensured by Legendre polynomials, mapped to the empirical distribution. We derive analytical series solutions for VIX futures and options using separation of variables to solve the Feynman-Kac PDE. Compared to the 3/2 model, our approach offers equal or superior accuracy and flexibility, providing an efficient, robust alternative for VIX pricing and risk management. Code and data are available at github.com/gagawjbytw/empirical-VIX. |
| title | Closed-form solutions for VIX derivatives in a Legendre empirical model |
| topic | Pricing of Securities Risk Management 91G20, 60J25, 65C30 |
| url | https://arxiv.org/abs/2309.08175 |