Modeling the BUX index by a novel stochastic differential equation

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