Perfect hedging in rough Heston models

The Quadratic Rough Heston Model and the Joint S&P 500/VIX Smile Calibration Problem

“…Though the quadratic rough Heston model is not Markovian in the variables (S, V ), it does admit an infinite dimensional Markovian representation. Inspired by the computations in [15], we obtain that for any t and t 0 positive…”

“…The process Z t may be understood as a weighted moving average of past price log returns. Indeed from Lemma A.1 in [15], we have that…”

“…So fast pricing of European options is possible, see [6,19]. In addition derivatives hedging is fully understood as shown in [15,16], see also [1,9].…”

A comparison principle between rough and non-rough Heston models—with applications to the volatility surface

“…The rough Heston model. We consider the rough Heston model [ER19,ER18] for a risk-neutral asset-price S with spot variance V, given by dS t " S t a V t dW t (2.1a)…”

“…Here, we focus on wing asymptotics (small-and large-strike) of implied volatility in the rough Heston model of [ER19] (see also [ER18]), which is becoming increasingly popular due to its tractability and its connections with affine processes (see [AJLP17,GKR19,KRLP18]). Starting with the results of [Lee04] (see also [BFL09]) it has become well-understood that wing asymptotics of implied volatility are intimately connected to moment explosions in the underlying stochastic model (see also [FKR10]).…”