I found this paper here https://arxiv.org/abs/1810.04868, "The Lifted Heston", but since I'm not an expert in stochastic volterra processes , nor in fractional ricatti equations, the math is beyond me. If anyone could explain to me step-by-step the process to simulate paths described in the paper (I know it's an approximation), or better yet, share a repo, I would greatly appreciate it.
Isn't this model just a bunch of classical Heston volatility processes, driven by the same Brownian motion? In this case, you can use some common schemes like Milstein. At least as a starter to toy with the model. If speed/accuracy is an issue, there probably exist some clever solutions as well.