# Simulating the same stock price with different methods/distributions

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.

• You can simulate whatever stock model you want. Simulation involves the creation of random variables. These random variables (note that a normal PC is not random at all) are feed into the model. You can view the model as a bridge between the random world and the real world. You usually use historical data to calibrate the model (i.e. recovering the model parameters, such as the mean and stdev in GBM). Jul 9, 2022 at 13:29
• That’s all clear to me. Let’s build on a GBM vs Heston model; what are the shared parameter that will allow us to compare the stock price simulations at the end of the exercise? Jul 9, 2022 at 13:49
• Well, I would gather ideas on: how to calibrate GBM and how to calibrate Heston. Heston is not trivial: degruyter.com/document/doi/10.1515/math-2017-0058/html Jul 9, 2022 at 15:10