Modeling the BUX index by a novel stochastic differential equation

Péter Alács, Imre M. Jánosi

Research output: Contribution to journalConference article

1 Citation (Scopus)


We present a new modeling approach for the fluctuations of the Budapest Stock Exchange index (BUX). The starting point is a statistical analysis of high resolution (5 s) data involving the first and second time-derivative of index values (index "velocities" and "accelerations"). Based on the results, we propose a simple stochastic differential equation with two noise terms, which explains the observed features but preserves linearity. The solution of the model based on this equation is a Lévy distribution. By introducing an additional (damping) term in the original equation, the stationary solution arises as a Lévy function with an exponential cut-off. A special characteristic of the 5 s BUX time series is the frequent presence of silent periods without index changes. The proposed equation can model also this feature by interpreting one of the noise terms as an intermittent Wiener process.

Original languageEnglish
Pages (from-to)273-278
Number of pages6
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1-2
Publication statusPublished - Oct 1 2001
EventApplication of Physics in Economic Modelling (NATO ARW) - Prague, Czech Republic
Duration: Feb 8 2001Feb 10 2001


  • Fluctuations
  • Statistics
  • Stochastic processes

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

Fingerprint Dive into the research topics of 'Modeling the BUX index by a novel stochastic differential equation'. Together they form a unique fingerprint.

  • Cite this