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December 2018 Perfect hedging in rough Heston models
Omar El Euch, Mathieu Rosenbaum
Ann. Appl. Probab. 28(6): 3813-3856 (December 2018). DOI: 10.1214/18-AAP1408

Abstract

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.

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Omar El Euch. Mathieu Rosenbaum. "Perfect hedging in rough Heston models." Ann. Appl. Probab. 28 (6) 3813 - 3856, December 2018. https://doi.org/10.1214/18-AAP1408

Information

Received: 1 March 2017; Revised: 1 June 2018; Published: December 2018
First available in Project Euclid: 8 October 2018

zbMATH: 06994407
MathSciNet: MR3861827
Digital Object Identifier: 10.1214/18-AAP1408

Subjects:
Primary: 26A33 , 60G22 , 60J25 , 91G20

Keywords: forward variance curve , fractional Brownian motion , fractional Riccati equations , Hawkes processes , limit theorems , rough Heston model , Rough volatility

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.28 • No. 6 • December 2018
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