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When reading a tutorail on extreme value theory, I once meet the following claim

Heavy tailed  marginals  are a preferable feature of models for financial time series.

Why finanical time series show a pattern of heavy tailed marginals? Are there any economic facts underlying this observation?

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For EVT, the more puzzling fact is that the "real" heavy tails do not scale with time... –  vanguard2k Jun 26 at 14:00

5 Answers 5

Volatility changes over time. Even if daily returns are normal, assuming the conditional volatility each day is known, the unconditional distribution of daily returns will have excess kurtosis. For example, if daily returns have a standard deviation of 1%, 90% of the time, and a standard deviation of 3%, 10% of the time, the presence of the high-volatility 3% standard deviation state will cause daily returns to exhibit fat tails. Mixtures of normals can be used to model distributions with tails that are heavier than normal.

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Extreme events in financial markets, like the crash of 1987, occur more frequently in the real world than a normal distribution would predict.

The economic facts that drive those extreme events are varying. Such extreme declines have been observed over many different time periods (Tulip-mania for instance), which suggests that it is more likely inherent to the fundamental nature of human beings. Nevertheless, such underlying biological forces need some economic conditions to manifest themselves. These are often unique to each specific crash (i.e., the economic conditions behind the crash of 1987 are different than the internet crash are different than the subprime crisis).

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A naive reason has been explained by Nassim Nicholas Taleb in his book titled Black Swan.

In a deeper look, one should be aware that no historical data analysis can truly estimate the real tail risk of financial markets. By the same token, standard deviation, max drawdown, expected shortfall, VaR, Conditional Var... No single or combination of such metrics can truly estimate the tail risk. Major News, market shocks and dislocations, randomness, etc can all lead to extreme behaviors and heavily tailed marginals.

I once wrote a thesis on Extreme Value Theory, and my work is basically concerned on modeling the occurrence of large-impact and low-probability extreme events on various domains. And our finding is that almost all extreme events will converge to a Generalized Pareto Distribution.

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It appears to be related to behavioral psychology.

In "space," there will be a statistical chance to two asteroids colliding, and a much larger number of near misses. But no asteroid will observe the "near miss" of two other asteroids and adjust its behavior or trajectory accordingly.

In human affairs, a "near miss" could produce just the result that was originally missed, as human beings panic and adjust their behavior to increase the possibility of a collision. Thus, "tail events" have to include not just the collisions that would have occurred naturally, but a number of (original) near misses that turned into "hits."

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Inhomogeneous time/sampling. Autocorrelation. Stochastic volatility. Jumps. Leverage.

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Providing more details will improve this answer. –  John Jun 27 at 20:16

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