2004/01/31 by A. Christian Silva, R. E. Prange, Richard E. Prange +1 · 3 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Econometrics #Economics #Exponential distribution #Exponential function #Financial Risk and Volatility Modeling #Gamma distribution #Gaussian #Log-normal distribution #Mathematical analysis #Mathematics #Mesoscopic physics #Physics #Power law #Probability distribution #Quantum mechanics #Statistical physics #Statistics #Stochastic processes and financial applications #Stylized fact #cond-mat.stat-mech #q-fin.ST
paper · pdf · doi:10.1016/j.physa.2004.06.122
published as Physica A 344, 227-235 (2004) · 7 pages, 12 plots, elsart.cls, submitted to the Proceedings of APFA-4. V.2: updated references
openalex publication_date 2004/07/24 · arxiv created 2004/07/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.