A maximum-entropy 'Boltzmann price' family interpolates between mid-price and weighted mid-price, and its imbalance-driven dynamics generate fat-tailed price changes that broadly resemble historical equity data.
Fat Tails in Financial Return Distributions Revisited: Evidence from the Korean Stock Market
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abstract
This study empirically re-examines fat tails in stock return distributions by applying statistical methods to an extensive dataset taken from the Korean stock market. The tails of the return distributions are shown to be much fatter in recent periods than in past periods and much fatter for small-capitalization stocks than for large-capitalization stocks. After controlling for the 1997 Korean foreign currency crisis and using the GARCH filter models to control for volatility clustering in the returns, the fat tails in the distribution of residuals are found to persist. We show that market crashes and volatility clustering may not sufficiently account for the existence of fat tails in return distributions. These findings are robust regardless of period or type of stock group.
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Boltzmann Price: Toward Understanding the Fair Price in High-Frequency Markets
A maximum-entropy 'Boltzmann price' family interpolates between mid-price and weighted mid-price, and its imbalance-driven dynamics generate fat-tailed price changes that broadly resemble historical equity data.