On the martingale property in the rough Bergomi model

Paul Gassiat

Papers from arXiv.org

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 $\rho \frac{1}{{1-\rho^2}}$, the $m$-th moment of the stock price is infinite at each positive time.

Date: 2018-11, Revised 2019-04
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