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2019 On the martingale property in the rough Bergomi model
Paul Gassiat
Electron. Commun. Probab. 24: 1-9 (2019). DOI: 10.1214/19-ECP239

Abstract

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 $\rho $ between the driving Brownian motions of the stock and the volatility is nonpositive. We also show that for each $\rho <0$ and $m> \frac{1} {{1-\rho ^{2}}}$, the $m$-th moment of the stock price is infinite at each positive time.

Citation

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Paul Gassiat. "On the martingale property in the rough Bergomi model." Electron. Commun. Probab. 24 1 - 9, 2019. https://doi.org/10.1214/19-ECP239

Information

Received: 3 December 2018; Accepted: 29 April 2019; Published: 2019
First available in Project Euclid: 14 June 2019

zbMATH: 07068657
MathSciNet: MR3962483
Digital Object Identifier: 10.1214/19-ECP239

Subjects:
Primary: 60G22, 60G44, 91G20

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