2023/03/13 by Eduardo Abi Jaber, Jaber, Eduardo Abi, Nathan De Carvalho +1 · 3 citations
Economics, Econometrics and Finance · Mathematics · #Computational Finance (q-fin.CP) #FOS: Economics and business #Financial Risk and Volatility Modeling #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2303.07222
openalex publication_date 2023/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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 ∈ \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 ≤ -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.