Reconciling rough volatility with jumps

Eduardo Abi Jaber () and Nathan de Carvalho
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Eduardo Abi Jaber: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Nathan de Carvalho: UPCité - Université Paris Cité

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Abstract: 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.

Keywords: Stochastic volatility; Heston model; Normal Inverse Gaussian; rough Heston model; Ricatti equations (search for similar items in EconPapers)
Date: 2024-09
Note: View the original document on HAL open archive server: https://hal.science/hal-04295416v2
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Citations: View citations in EconPapers (4)

Published in SIAM Journal on Financial Mathematics, 2024, 15 (3), pp.785-823

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