On the martingale property in the rough Bergomi model

Paul Gassiat

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arXiv · 1811.10935

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

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Paul Gassiat. 2019-04-30. On the martingale property in the rough Bergomi model. https://arxiv.org/abs/1811.10935

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