2009/12/22 by Miguel A. Fuentes, Miguel Fuentes, Austin Gerig +1 · 3 citations
Economics, Econometrics and Finance · Mathematics · #Biology #Brownian motion #Complex Systems and Time Series Analysis #Diffusion process #Econometrics #Economics #Financial Risk and Volatility Modeling #Financial economics #Geography #Geometric Brownian motion #Market Dynamics and Volatility #Mathematics #Standard deviation #Statistics #Stochastic process #Stochastic volatility #Stock (firearms) #Stock market #Stock price #Volatility (finance) #q-fin.ST
paper · pdf · doi:10.1371/journal.pone.0008243
published as PLoS ONE 4(12) e8243 (2009) · 4 pages, 3 figures
openalex publication_date 2009/12/22 · arxiv created 2009/12/30 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Many studies assume stock prices follow a random process known as geometric Brownian motion. Although approximately correct, this model fails to explain the frequent occurrence of extreme price movements, such as stock market crashes. Using a large collection of data from three different stock markets, we present evidence that a modification to the random model--adding a slow, but significant, fluctuation to the standard deviation of the process--accurately explains the probability of different-sized price changes, including the relative high frequency of extreme movements. Furthermore, we show that this process is similar across stocks so that their price fluctuations can be characterized by a single curve. Because the behavior of price fluctuations is rooted in the characteristics of volatility, we expect our results to bring increased interest to stochastic volatility models, and especially to those that can produce the properties of volatility reported here.