I would like to ask if we could simulate stock price paths with different methods/techniques.
What I mean is : say we have a specific stock price hence we can extract historical mean and standard deviation. Then one could use the GBM to simulate different trajectories under the normal distribution assumption.
Is it possible to create stock paths from the same stock price using the same initial ingredients (mean and std) but instead of using a simple GBM Monte Carlo, use Merton's Jump diffusion model or Heston's stochastic volatility? (I saw in other post that - for example- we cannot simulate using the T-distribution for fatter tails)
I ask if is possible in the context that I want then to compare the results say of a VaR model and the level of it for different simulation techniques. I presume to be able to compare the results we have to use the same main ingredients.
Happy to have your feedback and explain more in detail if not clear.