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On the martingale property in the rough bergomi model. (English) Zbl 07068657
Summary: 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.

MSC:
 60G44 Martingales with continuous parameter 60G22 Fractional processes, including fractional Brownian motion 91G20 Derivative securities (option pricing, hedging, etc.)
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References:
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