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On the martingale property in the rough Bergomi model

Gassiat, Paul (2019), On the martingale property in the rough Bergomi model, Electronic Communications in Probability, 24, p. 9. 10.1214/19-ECP239

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Type
Article accepté pour publication ou publié
Date
2019
Journal name
Electronic Communications in Probability
Volume
24
Publisher
Institute of Mathematical Statistics
Pages
9
Publication identifier
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Author(s)
Gassiat, Paul
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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.
Subjects / Keywords
rough volatility; martingale property