Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact

Details Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact

2004-01-14

arxiv.org/abs/cond-mat/0401225v2

Physica A 344, 227-235 (2004)

Physics

Condensed Matter

Statistical Mechanics

7 pages, 12 plots, elsart.cls, submitted to the Proceedings of APFA-4. V.2: updated references

Scientific paper

10.1016/j.physa.2004.06.122

We study the probability distribution of stock returns at mesoscopic time lags (return horizons) ranging from about an hour to about a month. While at shorter microscopic time lags the distribution has power-law tails, for mesoscopic times the bulk of the distribution (more than 99% of the probability) follows an exponential law. The slope of the exponential function is determined by the variance of returns, which increases proportionally to the time lag. At longer times, the exponential law continuously evolves into Gaussian distribution. The exponential-to-Gaussian crossover is well described by the analytical solution of the Heston model with stochastic volatility.

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