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On the martingale property in the rough Bergomi model

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1811.10935.pdf (146.2Kb)
Date
2019
Dewey
Probabilités et mathématiques appliquées
Sujet
rough volatility; martingale property
Journal issue
Electronic Communications in Probability
Volume
24
Publication date
06-2019
Article pages
9
Publisher
Institute of Mathematical Statistics
DOI
http://dx.doi.org/10.1214/19-ECP239
URI
https://basepub.dauphine.fr/handle/123456789/20350
Collections
  • CEREMADE : Publications
Metadata
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Author
Gassiat, Paul
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Article accepté pour publication ou publié
Abstract (EN)
We consider a class of fractional stochastic volatility models (including the so-called rough Bergomi model), where the volatility is a superlinear function of a fractional Gaussian process. We show that the stock price is a true martingale if and only if the correlation ρ between the driving Brownian motions of the stock and the volatility is nonpositive. We also show that for each ρ<0 and m>11−ρ2, the m-th moment of the stock price is infinite at each positive time.

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