Perfect hedging in rough Heston models

By Omar El Euch, Mathieu Rosenbaum. The Annals of Applied Probability, 2017

156 citations recorded by the source corpus.

Rough volatility models are known to reproduce the behavior of historical volatility data while at the same time fitting the volatility surface remarkably well, with very few parameters. However, managing the risks of derivatives under rough volatility can be intricate since the dynamics involve fractional Brownian motion. We show in this paper that surprisingly enough, explicit hedging strategies can be obtained in the case of rough Heston models. The replicating portfolios contain the underlying asset and the forward variance curve, and lead to perfect hedging (at least theoretically). From a probabilistic point of view, our study enables us to disentangle the infinite-dimensional Markovian structure associated to rough volatility models.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/03def6581fdab15051fb05bfb6ea2fdd467308c3

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Citations in the corpus

A regularity structure for rough volatility (2017, methodology): “Rough volatility not only provides remarkable fits to both time series and option pricing problems, it also has a market microstructure justification: starting with a Hawkes process model, Rosenbaum and coworkers [16, 17, 18] find in the scaling limit f, g, h such that”
No‐arbitrage implies power‐law market impact and rough volatility (2018, background): “1 in [12], we deduce the following equality in law: Nt L = N t + N0 t ∑”
The characteristic function of rough Heston models (2016, methodology): “4 Actually, using a more complex framework of Hawkes processes, one can show that the results still hold for any 𝜌 ∈ [−1, 1]; see El Euch and Rosenbaum (2018).”
The Quadratic Rough Heston Model and the Joint S&P 500/VIX Smile Calibration Problem (2020, methodology): “Inspired by the computations in [15], we obtain that for any t and t0 positive”
Markovian structure of the Volterra Heston model (2018, methodology): “In [7], the authors highlight the crucial role of (1.”
Generalized Feller processes and Markovian lifts of stochastic Volterra processes: the affine case (2018, background): “st classical. 1. Introduction In the realm of the recent discovery of rough volatility models (see e.g., [4, 21, 15, 16]), stochastic Volterra processes have been studied extensively, for instance in [24, 3, 17] and the references therein. It is well known that Markovian lifts of such processes exis”