The Annals of Applied Probability

Perfect hedging in rough Heston models

Omar El Euch and Mathieu Rosenbaum

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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.

Article information

Source
Ann. Appl. Probab., Volume 28, Number 6 (2018), 3813-3856.

Dates
Received: March 2017
Revised: June 2018
First available in Project Euclid: 8 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1538985636

Digital Object Identifier
doi:10.1214/18-AAP1408

Mathematical Reviews number (MathSciNet)
MR3861827

Zentralblatt MATH identifier
06994407

Subjects
Primary: 91G20: Derivative securities 26A33: Fractional derivatives and integrals 60G22: Fractional processes, including fractional Brownian motion 60J25: Continuous-time Markov processes on general state spaces

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

Citation

El Euch, Omar; Rosenbaum, Mathieu. Perfect hedging in rough Heston models. Ann. Appl. Probab. 28 (2018), no. 6, 3813--3856. doi:10.1214/18-AAP1408. https://projecteuclid.org/euclid.aoap/1538985636


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