Stochastic local volatility models and the Wei-Norman factorization method

In this paper, we show that a time-dependent local stochastic volatility (SLV) model can be reduced to system of autonomous PDEs solved using the heat kernel, by means Wei-Norman factorization method and Lie algebraic techniques. Then, compare results traditional Monte Carlo simulations with explicit solutions obtained said This approach is new in literature and, addition reducing non-autonomous problem into an one, allows for shorter time numerical computations.