A dynamical model describing stock market price distributions
Abstract
High frequency data in finance have led to a deeper understanding on probability distributions of market prices. Several facts seem to be well stablished by empirical evidence. Specifically, probability distributions have the following properties: (i) They are not Gaussian and their center is well adjusted by Levy distributions. (ii) They are long-tailed but have finite moments of any order. (iii) They are self-similar on many time scales. Finally, (iv) at small time scales, price volatility follows a non-diffusive behavior. We extend Merton's ideas on speculative price formation and present a dynamical model resulting in a characteristic function that explains in a natural way all of the above features. The knowledge of such distribution opens a new and useful way of quantifying financial risk. The results of the model agree -with high degree of accuracy- with empirical data taken from historical records of the Standard & Poor's 500 cash index.
Keywords
Cite
@article{arxiv.cond-mat/0003357,
title = {A dynamical model describing stock market price distributions},
author = {Jaume Masoliver and Miquel Montero and Josep M. Porra},
journal= {arXiv preprint arXiv:cond-mat/0003357},
year = {2009}
}
Comments
11 pages, 2 eps figures, elsart, to be published in Physica A