Fat Tail Query

[govigovi]

Can you please help me with the answer of this question with explanation ?

The problem of fat tails when measuing volatility is least likely in -
1 In an unstable distribution
in a conditional distribution
in a regime switching model
in an unconditional distribution

 

[nc27]

You observe fat tails in a distribution most likely when unconditional distribution of returns is not normally shaped and you conditionally assume the returns are normal (you inputs mean and volatility parameters as being true). That is, you assume about 99.7% of all variations falls within three standard deviations of the mean and therefore there is only a 0.3% chance of an extreme event occurring. This property is important because many financial models such as Modern Portfolio Theory, Efficient Markets and BSM pricing models all assume normality.
Also you do assume in the normal distribution that volatility is a constant (fixed over time as in the BSM theory for example...) what if sigma is a function of time that is we have volatility = sigma(t) ... volatility is not constant over time

some reading source ...

The dangerous disregard for fat tails in quantitative finance | Macrosynergy Research

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