Simulation of the Heston stochastic local volatility model: implicit and explicit approaches

The Heston stochastic-local volatility (HSLV) model is widely used to capture both market calibration and realistic volatility dynamics, but simulating its CIR-type variance process is numerically challenging.This paper compare two alternative schemes for HSLV simulation: the truncated Euler method and the backward Euler method with the conventional Euler and almost exact simulation methods in \cite{van2014heston} by using a Monte Carlo method.Numerical results show that the truncated method achieves strong convergence and remains robust under high volatility, while the backward method provides the smallest errors and most stable performance in stress scenarios, though at higher computational cost.