PERFECT HEDGING IN ROUGH HESTON MODELS

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 fra...

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Bibliographic Details
Published in:The Annals of applied probability Vol. 28; no. 6; pp. 3813 - 3856
Main Authors: Euch, Omar El, Rosenbaum, Mathieu
Format: Journal Article
Language:English
Published: Hayward Institute of Mathematical Statistics 01-12-2018
Institute of Mathematical Statistics (IMS)
Subjects:
Brownian motion
Hedging
Markov analysis
Markov chains
Mathematics
Portfolios
Probability
Replication
Volatility
Online Access:Get full text
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Summary: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.
ISSN:1050-5164
2168-8737
DOI:10.1214/18-AAP1408