Pricing and calibration in the 4-factor path-dependent volatility model
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915168604127232 |
|---|---|
| author | Gazzani, Guido Guyon, Julien |
| author_facet | Gazzani, Guido Guyon, Julien |
| contents | We consider the path-dependent volatility (PDV) model of Guyon and Lekeufack (2023), where the instantaneous volatility is a linear combination of a weighted sum of past returns and the square root of a weighted sum of past squared returns. We discuss the influence of an additional parameter that unlocks enough volatility on the upside to reproduce the implied volatility smiles of S\&P 500 and VIX options. This PDV model, motivated by empirical studies, comes with computational challenges, especially in relation to VIX options pricing and calibration. We propose an accurate \emph{pathwise} neural network approximation of the VIX which leverages on the Markovianity of the 4-factor version of the model. The VIX is learned pathwise as a function of the Markovian factors and the model parameters. We use this approximation to tackle the joint calibration of S\&P 500 and VIX options, quickly sample VIX paths, and price derivatives that jointly depend on S\&P 500 and VIX. As an interesting aside, we also show that this \emph{time-homogeneous}, low-parametric, Markovian PDV model is able to fit the whole surface of S\&P 500 implied volatilities remarkably well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02319 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pricing and calibration in the 4-factor path-dependent volatility model Gazzani, Guido Guyon, Julien Computational Finance Mathematical Finance Pricing of Securities 91B70, 91G20, 91G30, 91G60, 65C20 We consider the path-dependent volatility (PDV) model of Guyon and Lekeufack (2023), where the instantaneous volatility is a linear combination of a weighted sum of past returns and the square root of a weighted sum of past squared returns. We discuss the influence of an additional parameter that unlocks enough volatility on the upside to reproduce the implied volatility smiles of S\&P 500 and VIX options. This PDV model, motivated by empirical studies, comes with computational challenges, especially in relation to VIX options pricing and calibration. We propose an accurate \emph{pathwise} neural network approximation of the VIX which leverages on the Markovianity of the 4-factor version of the model. The VIX is learned pathwise as a function of the Markovian factors and the model parameters. We use this approximation to tackle the joint calibration of S\&P 500 and VIX options, quickly sample VIX paths, and price derivatives that jointly depend on S\&P 500 and VIX. As an interesting aside, we also show that this \emph{time-homogeneous}, low-parametric, Markovian PDV model is able to fit the whole surface of S\&P 500 implied volatilities remarkably well. |
| title | Pricing and calibration in the 4-factor path-dependent volatility model |
| topic | Computational Finance Mathematical Finance Pricing of Securities 91B70, 91G20, 91G30, 91G60, 65C20 |
| url | https://arxiv.org/abs/2406.02319 |