On the martingale property in the rough Bergomi model

2018/11/27 by Paul Gassiat, Gassiat, Paul · 2 citations
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.1811.10935

openalex publication_date 2018/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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> (1)/(1-ρ²), the m-th moment of the stock price is infinite at each positive time.

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