Option pricing under model involving slow growth volatility

In this paper, we present a new model of the European option price, it is about a model involving slow growth volatility. The SGV model (slow growth volatility model) is the name of the new model considered in this manuscript. The mathematical analysis shows that one has to resort to a degenerate parabolic equation, the resolution of which gives the price of the European option as a function of the time, the price of the underlying asset and the instantaneous volatility.