Comparing Stock Path Simulations Across Return Distributions

Summary

The document asks whether stock price paths can be simulated with different models while holding the initial price and historical mean and standard deviation fixed. It names geometric Brownian motion (GBM), Merton jump diffusion, and Heston stochastic volatility as alternatives, and raises the possibility of using heavier-tailed return distributions to compare value-at-risk estimates.

It does not provide a model specification, calibration procedure, comparison, or empirical results; it is a question seeking guidance. A key methodological issue is that matching a mean and standard deviation alone may not make models comparable, since they can differ in dynamics and additional parameters. The document therefore frames a useful modeling question but leaves unresolved how to define comparable inputs, calibrate each model, or interpret differences in VaR.

Key ideas

• The document proposes comparing simulated stock paths from GBM, jump diffusion, and stochastic volatility models.
• It asks whether models can share an initial price and historical mean and standard deviation.
• It identifies value at risk as a possible output for comparing simulation methods.
• It provides no calibration method or evidence that matching two historical statistics makes the models comparable.

Tags

# Simulating the same stock price with different methods/distributions


# 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.

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