On the Guyon-Lekeufack Volatility Model
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913412506714112 |
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| author | Nutz, Marcel Valdevenito, Andrés Riveros |
| author_facet | Nutz, Marcel Valdevenito, Andrés Riveros |
| contents | Guyon and Lekeufack recently proposed a path-dependent volatility model and documented its excellent performance in fitting market data and capturing stylized facts. The instantaneous volatility is modeled as a linear combination of two processes, one is an integral of weighted past price returns and the other is the square-root of an integral of weighted past squared volatility. Each of the weightings is built using two exponential kernels reflecting long and short memory. Mathematically, the model is a coupled system of four stochastic differential equations. Our main result is the wellposedness of this system: the model has a unique strong (non-explosive) solution for all parameter values. We also study the positivity of the resulting volatility process and the martingale property of the associated exponential price process. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_01319 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Guyon-Lekeufack Volatility Model Nutz, Marcel Valdevenito, Andrés Riveros Pricing of Securities Probability 60H10, 91G20 Guyon and Lekeufack recently proposed a path-dependent volatility model and documented its excellent performance in fitting market data and capturing stylized facts. The instantaneous volatility is modeled as a linear combination of two processes, one is an integral of weighted past price returns and the other is the square-root of an integral of weighted past squared volatility. Each of the weightings is built using two exponential kernels reflecting long and short memory. Mathematically, the model is a coupled system of four stochastic differential equations. Our main result is the wellposedness of this system: the model has a unique strong (non-explosive) solution for all parameter values. We also study the positivity of the resulting volatility process and the martingale property of the associated exponential price process. |
| title | On the Guyon-Lekeufack Volatility Model |
| topic | Pricing of Securities Probability 60H10, 91G20 |
| url | https://arxiv.org/abs/2307.01319 |