Stochastic modelling of herd behaviour indices

This paper proposes different diffusion processes to model herd behaviour indices such as the Herd Behaviour Index (HIX). These models arise by combining popular mean-reverting processes with simple algebraic functions mapping the definition domain of the underlying mean-reverting process to the unit interval. The so obtained Itô processes preserve, to some extent, the mean-reverting trend of the underlying process while satisfying the fundamental properties of the so-called herd behaviour indices. In a numerical study, we calibrate the different model settings to time series data for a period spanning from January 2000 until October 2009 and investigate their ability to predict the future behaviour of herd behaviour indices.