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
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