Electronic Communications in Probability

On the martingale property in the rough Bergomi model

Paul Gassiat

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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.

Article information

Electron. Commun. Probab., Volume 24 (2019), paper no. 33, 9 pp.

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

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Primary: 60G44: Martingales with continuous parameter 60G22: Fractional processes, including fractional Brownian motion 91G20: Derivative securities

rough volatility martingale property

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Gassiat, Paul. On the martingale property in the rough Bergomi model. Electron. Commun. Probab. 24 (2019), paper no. 33, 9 pp. doi:10.1214/19-ECP239. https://projecteuclid.org/euclid.ecp/1560477645

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