Stochastic modelling of herd behaviour indicesStochastic modelling of herd behaviour indices
Faculty of Sciences. Mathematics and Computer Science
Applied mathematics and numerical analysis
Quantitative finance. - London
15(2015):12, p. 1963-1977
University of Antwerp
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.