A dynamical model describing stock market price distributions

Details A dynamical model describing stock market price distributions A dynamical model describing stock market price distributions

2000-03-22

arxiv.org/abs/cond-mat/0003357v1

Physica A 283 (2000) 559-567

Physics

Condensed Matter

Statistical Mechanics

11 pages, 2 eps figures, elsart, to be published in Physica A

Scientific paper

10.1016/S0378-4371(00)00117-5

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.

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