Reconciling rough volatility with jumps
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916389730648064 |
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| author | Jaber, Eduardo Abi De Carvalho, Nathan |
| author_facet | Jaber, Eduardo Abi De Carvalho, Nathan |
| contents | We reconcile rough volatility models and jump models using a class of reversionary Heston models with fast mean reversions and large vol-of-vols. Starting from hyper-rough Heston models with a Hurst index $H \in (-1/2,1/2)$, we derive a Markovian approximating class of one dimensional reversionary Heston-type models. Such proxies encode a trade-off between an exploding vol-of-vol and a fast mean-reversion speed controlled by a reversionary time-scale $ε>0$ and an unconstrained parameter $H \in \mathbb R$. Sending $ε$ to 0 yields convergence of the reversionary Heston model towards different explicit asymptotic regimes based on the value of the parameter H. In particular, for $H \leq -1/2$, the reversionary Heston model converges to a class of Lévy jump processes of Normal Inverse Gaussian type. Numerical illustrations show that the reversionary Heston model is capable of generating at-the-money skews similar to the ones generated by rough, hyper-rough and jump models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_07222 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Reconciling rough volatility with jumps Jaber, Eduardo Abi De Carvalho, Nathan Mathematical Finance Computational Finance We reconcile rough volatility models and jump models using a class of reversionary Heston models with fast mean reversions and large vol-of-vols. Starting from hyper-rough Heston models with a Hurst index $H \in (-1/2,1/2)$, we derive a Markovian approximating class of one dimensional reversionary Heston-type models. Such proxies encode a trade-off between an exploding vol-of-vol and a fast mean-reversion speed controlled by a reversionary time-scale $ε>0$ and an unconstrained parameter $H \in \mathbb R$. Sending $ε$ to 0 yields convergence of the reversionary Heston model towards different explicit asymptotic regimes based on the value of the parameter H. In particular, for $H \leq -1/2$, the reversionary Heston model converges to a class of Lévy jump processes of Normal Inverse Gaussian type. Numerical illustrations show that the reversionary Heston model is capable of generating at-the-money skews similar to the ones generated by rough, hyper-rough and jump models. |
| title | Reconciling rough volatility with jumps |
| topic | Mathematical Finance Computational Finance |
| url | https://arxiv.org/abs/2303.07222 |