In this paper, we employ multifractal detrended cross-correlation analysis (MF-DCCA) to study the cross-correlation between closing price and trading volume and the multifractal characteristics of the relationship. The results show that the price, volume and price–volume cross-correlation in the rebar futures market have significant multifractal features. We find that the multifractal characteristics of price–volume cross-correlation are derived from long-term correlation and fat-tailed distribution. However, MF-DCCA cannot be used to explore the price–volume cross-correlation under different market trends (upwards or downwards). Therefore, we further adopt multifractal asymmetric detrended cross-correlation analysis (MF-ADCCA) to explore the asymmetric multifractal characteristics of price–volume cross-correlation. The empirical results show that the price–volume cross-correlation in the rebar futures market has significant asymmetric multifractality. Specifically, the asymmetry of the price–volume cross-correlation is more robust for both the price changes and the volume changes in a downtrend than that in an uptrend, indicating that the downward market tends to be more complex and riskier than the upward market in Shanghai Futures Exchange (SHFE) rebar futures market. Therefore, investors should pay extra attention to the downward market of the rebar futures and make reasonable investment strategies according to their risk appetite.
In this paper, we use the finite difference methods to explore step-down Equity Linked Securities (ELS) options under the fractional Black-Scholes model. We establish Crank-Nicolson scheme under one asset and study the impact of Hurst exponent (H) on return of repayment under fixed stock price. We also explore the impact of stock price on return of repayment under different H. Through numerical experiments, it is found that the return of repayment of options is related to H, and the result of difference scheme will increase with the increase of H. In the case of two assets, we establish implicit scheme, and in the case of three assets, we use operator splitting method (OSM) method to establish semi-implicit scheme. We get the result that the H also influences the return of repayment in two and three assets. We also conduct Greeks analysis. Through Greeks analysis, we find that the long-term correlation of stocks has a huge impact on investment gains or losses. Therefore, we take historical volatility (fractal exponents) into account which can significantly reduce risk and increase revenue for investors.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.