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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!

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  • $\begingroup$ How are you calibrating your marginal logistic distribution, and how are you specifying and calibrating their cointegration? $\endgroup$ – Brian B Dec 18 '15 at 18:41
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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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