Levy’s stable distribution for stock crash detecting

Abstract

In this paper we study the possibility of construction indicators-precursors relying on one of the most power-law tailed distributions – Levy’s stable distribution. Here, we apply Levy’s parameters for 29 stock indices for the period from 1 March 2000 to 28 March 2019 daily values and show their effectiveness as indicators of crisis states on the example of Dow Jones Industrial Average index for the period from 2 January 1920 to 2019. In spite of popularity of the Gaussian distribution in financial modeling, we demonstrated that Levy’s stable distribution is more suitable due to its theoretical reasons and analysis results. And finally, we conclude that stability α and skewness β parameters of Levy’s stable distribution which demonstrate characteristic behavior for crash and critical states, can serve as an indicator-precursors of unstable states.