  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 $\epsilon>0$ and an unconstrained parameter $H \in \mathbb R$.
Sending $\epsilon$ 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 L\'evy 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.
