Dynamic behaviors and measurements of financial market crash rate

Abstract This paper proposes the conditional crash rate (CCR) to study the degree of financial market crisis and evaluate the risk of financial market crash, based on maximum drawdown and escape rate. It is found that the CCR of stock price in financial market is equivalent to the escape rate of the drawdown time series corresponding to price series. Based on the mean escape rate, the analytical solution of CCR of financial market of stock price described by Black–Scholes model is obtained. For the CCR, empirical researches show that the theoretical results of the Heston model are in good agreement with the results of the real financial data of the SP (ii) we can find critical phenomena, resonance and inverse resonance behaviors in the function of CCR vs. mean reversion of volatility; (ii) the parameter variation induces the appearance of noise enhancement stability in the function of CCR vs. amplitude of volatility fluctuation.