Choosing Return Processes for Logistic-Distribution Monte Carlo VaR

Summary

The document considers changing a Monte Carlo Value at Risk model from geometric Brownian motion with normal shocks to one using logistic-distributed returns. The question is whether replacing the standard normal variates is appropriate and whether the resulting higher VaR is meaningful. The response does not endorse that substitution or explain how a logistic shock process would affect price dynamics, calibration, or risk estimates.

As alternatives for non-Gaussian returns, it points to Lévy processes and mentions Student’s t returns for fatter tails and the variance gamma process. It also questions the rationale for choosing a logistic distribution, noting that the document supplies no reference or supporting evidence. This is a brief pointer rather than a modeling recipe: it gives no distribution-fitting procedure, simulation details, or empirical comparison. Any proposed process would still need to be specified and calibrated to the portfolio and horizon before its VaR can be assessed.

Key ideas

• Replacing normal shocks with logistic variates is raised as a modeling question, not established as a sound price process.
• The response suggests Lévy-process models as a broad family of non-Gaussian alternatives.
• Student’s t returns and variance gamma are named as possible models for heavier-tailed behavior.
• The logistic assumption is unsupported in the document, and no calibration or VaR comparison is provided.

Tags

# Monte Carlo VaR assuming logistic distribution


# Monte Carlo VaR assuming logistic distribution












I have a Monte Carlo model which measures the Value at Risk (VaR) for given portfolio. I use the geometric brownian motion to model the prices. But let's say I assumed the returns of prices follow the logistic distribution and thereby I want to change the model.

Would it be correct to substitute the variable that represents standard normal variate with logistic variate? Or would it better to use other process to model prices?

I substituted the logistic variates to the model but I think VaR is too high compared to the previous assumption.

Any help would be appreciated!

## Answer by Richi Wa (score 1)

https://quant.stackexchange.com/a/21307

If you want to get rid of the Gaussian returns, then you could have a look at Lévy processes. You could assume a t-distribution for returns for fatter tails or you could have a look at so called variance gamma.

I have never seen somebody using the logistic distribution to model asset returns (this one ?) Where do you have this idea from (any reference)?

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