Reconciling rough volatility with jumps - Département de mathématiques appliquées
Article Dans Une Revue SIAM Journal on Financial Mathematics Année : 2024

Reconciling rough volatility with jumps

Résumé

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 ∈ (−1/2, 1/2), we derive a Markovian approximating class of one dimensional reversionary Hestontype models. Such proxies encode a trade-off between an exploding vol-of-vol and a fast mean-reversion speed controlled by a reversionary timescale ϵ > 0 and an unconstrained parameter H ∈ 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 ≤ −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.
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Dates et versions

hal-04295416 , version 1 (20-11-2023)
hal-04295416 , version 2 (11-09-2024)

Identifiants

  • HAL Id : hal-04295416 , version 2

Citer

Eduardo Abi Jaber, Nathan de Carvalho. Reconciling rough volatility with jumps. SIAM Journal on Financial Mathematics, 2024, 15 (3), pp.785-823. ⟨hal-04295416v2⟩
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