Eur. Phys. J. B 21, 155-158 (2001)
https://doi.org/10.1007/PL00011121

Anomalous scaling of stock price dynamics within ARCH-models

¹ Dipartimento di Fisica, Universitá di Milano, Via Celoria 16, 20133 Milano, Italy
² INFN, Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
³ Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, 01187 Dresden, Germany

Corresponding author: ^a porto@mpipks-dresden.mpg.de

Received: 12 October 2000
Revised: 5 February 2001
Published online: 15 May 2001

Abstract

We show that autoregressive-conditional-heteroskedasticity (ARCH) models can encompass the observed anomalous scaling properties of stock price dynamics remarkably well. We find that with a suitable choice of parameters, simple ARCH models can reproduce the non-standard scaling behavior of the central part of the probability distribution functions of stock prices at different time horizons, as empirically found for the Standard & Poors 500 (S&P 500) index data, but fail to reproduce the shape of the S&P 500 distribution, in particular at the smallest time horizon (1 min). A linear version of ARCH processes, denoted here as LARCH models, still preserving the anomalies observed, permits to fit the 1 min S&P 500 distribution more accurately.