Levy distribution parameters as precursors of crisis phenomena

Abstract

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. 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 moving window based procedure for calculation of Levy’s parameters - a - stability and /?- skewness for daily values of Dow Jones Industrial Average (from 1 March 2000 to 28 March 2019), the gold price (from 1 April 1968 to 8 May 2019) and Brent crude oil price (from 2 January 1986 to 6 May 2019) which show their effectiveness as indicators of crisis states. For the construction of the indicators, were selected time series of and, accordingly, for oil. Dow Jones’ time series has the period from 2 January 1920 to 2019. We conclude that a and /3 parameters of Levy’s stable distribution of the observed assets, which demonstrate characteristic behavior for crash and critical states, can serve as an indicator-precursors of the unstable states.