Before revision: We introduce the notion of rough local stochastic volatility models , extending the classical concept to the case where volatility is driven by some Volterra process. In this setting, we show that the pricing function is the solution to a path-dependent PDE , for which we develop a numerical scheme based on Deep Learning techniques.
After revision: We introduce the notion of rough local stochastic volatility models . We show that the pricing function is the solution to a path-dependent PDE , for which we develop a numerical scheme based on Deep Learning techniques.