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Does this have any relation to the symmetry of the normal distribution?

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Heavier tails, or a higher probability of extreme outlier values, meaning the investor is more likely to experience extreme events (e.g. tail losses).

EDIT: @noob2, valid point, see this article on modelling and forecasting the kurtosis and returns distribution of financial markets: irrational fractional Brownian motion model approach

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  • $\begingroup$ In another question, you have asked what are the alternatives to GBM that can be used in option valuation. One reason people have developed such alternatives is they feel GBM is inadequate for modeling real world stock markets because NOT leptokurtic like the real markets are. $\endgroup$ – noob2 Jul 11 '20 at 14:08

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