Roles of GARCH and ARCH effects on the stability in stock market crash

Abstract

We theoretically stochastically simulate and empirically analyze the escape process of stock market price non-equilibrium dynamics under the influence of GARCH and ARCH effects, and explore the impact of ARCH and GARCH effects on stock market stability. Based on the nonlinear GARCH model of econophysics, and combined with GARCH and ARCH effects of volatility, we propose a delay stochastic monostable potential model. We use the mean escape time, or mean hitting time, as an indicator for measuring price stability, as first introduced in Valenti D. et al., Phys. Rev. E, 97 (2018) 062307. Based on the comparative analysis of actual Chinese A-share data, the theoretical and empirical findings of this paper are as follows: 1) The theoretical simulation results and actual data are consistent. 2) There exist optimal GARCH and ARCH effects maximally enhancing stock market stability.