I want to price a path-dependent option (let's say for example an arithmetic average Asian option) under a Heston model. In a Black-Scholes setup, I use forward volatilities to do so. I want to apply the same idea with a Heston model as I'm not only interested in the terminal state of the underlying process, but also in the path by which the final process is reached. So I assume I need to use forward parameters and the only idea I have so far is obtaining time dependent parameters ( Piecewise constant actually) using Elices's Paper (https://arxiv.org/abs/0708.2020) and then using them in a Monte Carlo scheme.
Question : Is there a way to do the same with only static parameters ( 1 set of 5 parameters) using any discrete scheme for Heston such us Milstein or QE.