Stochastic resonance of volatility influenced by price periodic information in financial market

Abstract

General researches show that all kinds of random risk information and periodic information in the financial system are mainly transmitted to the asset price through influencing the volatility, thus impacting the whole market. So can the periodic information and random factors in the price be transmitted to the volatility in reverse and cause volatility changes? Hence, in this paper, we investigate the stochastic resonance of volatility which is influenced by price periodic information in financial market, based on our proposed periodic Brownian Motion model and absolute return volatility. The parameter estimation of the periodic Brownian Motion model is obtained by minimizing the mean square deviation between the theoretical and empirical return distributions for the CSI300 data set. The good agreements of the probability density functions of the price returns, realized volatility (RV) at 5 minutes, RV at 15 minutes and absolute return volatility between theoretical and empirical calculation are found. After simulating the absolute return volatility and signal power amplification (SPA) of volatility via periodic Brownian Motion model, the results indicated that (i) single and double inverse resonance phenomena can be observed in the function of SPA versus random information intensity or economic growth rate; (ii) multiple inverse resonance phenomena can be also observed for SPA versus frequency of periodic information. The results imply that the transmission of stochastic factors and periodic information is not only from the volatility to the price, but also from the price to the volatility.