The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 28, Number 6 (2018), 3813-3856.
Perfect hedging in rough Heston models
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.
Ann. Appl. Probab., Volume 28, Number 6 (2018), 3813-3856.
Received: March 2017
Revised: June 2018
First available in Project Euclid: 8 October 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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