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We investigate the stochastic resonance of periodic volatility in two financial markets with stock crashes for Dow Jones component stocks and Hang Seng index, based on the modified Heston model with an effective potential to describe the stock crashes. We introduce a cosine term to Heston model and develop a modified Heston model with periodic stochastic volatility for capturing the periodicity of the volatility process or volatility clustering which was observed in historical financial data sets. The proposed model was tested against Dow Jones industrial and Hang Seng index data. The experimental results demonstrate that the proposed model fits the historical data well when compared with the original Heston model. The signal power amplification (SPA) is calculated and studied to investigate the stochastic resonance of the proposed dynamic system. Experimental results suggest that: (i) optimal values of volatility parameters can be identified which maximize the effects of systematic and non-systematic randomness to the market periodicity; (ii) different values of correlation strength between noise sources will cause critical phenomenon and induce single or multiple resonances. [ABSTRACT FROM AUTHOR]

In this article we investigate the occurrence of stock market crash in an economy cycle. Bayesian approach, Heston model and statistical–physical method are considered. Specifically, Heston model and an effective potential are employed to address the dynamic changes of stock price. Bayesian approach has been utilized to estimate the Heston model's unknown parameters. Statistical physical method is used to investigate the occurrence of stock market crash by calculating the mean time-limited crash rate. The real financial data from the Shanghai Composite Index is analyzed with the proposed methods. The mean time-limited crash rate of stock price is used to describe the occurrence of stock market crash in an economy cycle. The monotonous and nonmonotonous behaviors are observed in the behavior of the mean time-limited crash rate versus volatility of stock for various cross correlation coefficient between volatility and price. Also a minimum occurrence of stock market crash matching an optimal volatility is discovered. [ABSTRACT FROM AUTHOR]

The stability of portfolio investment in stock market crashes with Markowitz portfolio is investigated by the method of theoretical and empirical simulation. From numerical simulation of the mean escape time (MET), we conclude that: (i) The increasing number of stocks in Markowitz portfolio induces a maximum in the curve of MET versus the initial position; (ii) A critical value of in the behavior of MET versus the long-run variance or amplitude of volatility fluctuations maximumlly enhances the stability of portfolio investment. When takes value below the critical value, the increasing enhances the stability of portfolio investment, but restrains it when takes value above the critical value. In addition, a good agreement of both the MET and probability density functions of returns is found between real data and theoretical results. [ABSTRACT FROM AUTHOR]