Before revision:  We show they admit the same limit dynamics in the regime of low fluctuations of the volatility process, under which we derive the expressions of the characteristic function and the first four cumulants for the risk neutral probability measure. This allows us to obtain a semi-closed form for European option prices , based on Lewis ' approach.
After revision:  We show they admit the same limit dynamics in the regime of low fluctuations of the volatility process, under which we derive the expressions of the characteristic function and the first four cumulants for the risk neutral probability density. Its knowledge allows us to obtain a semi-closed form for European option prices , based on Lewis ' approach.