Electronic Communications in Probability

On the martingale property in the rough Bergomi model

Paul Gassiat

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1560477645

Digital Object Identifier
doi:10.1214/19-ECP239

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

Keywords
rough volatility martingale property

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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