Multiscale Behavior Properties And Risk Analysis Of Capital Markets

Study on random distribution characteristics of returns has always been one of the most challenging problems in finance. Traditional researches in this field are commonly made under the circumstance of monoscale. However, in recent years, physicists have introduced multiscale of being an important concept in econophysics to financial economics, and have achieved fruits of interesting results quite different from what the previous studies have made. All these valuable works have explored the development of researches in the fields greatly.This paper investigates the internal microstructure and controlling mechanism of capital markets through systematically studying the multiscale behaviors of returns. And then the multiscale volatility model is constructed to further research the risk measurement and control for asserts over the different time scale. This paper consists of seven chapters involving the four main sections. Firstly, the paper investigates the power-law properties and criticality of returns especially for the respective distributions of negative and positive tails, and discusses their generality. And the correlation properties of different volatility amplitudes of returns are analyzed based on the framework of multifractal detrended fluctuation. Secondly, the paper analyzes the controlling strength of three special correlations of maintaining the multiscale power-law distribution respectively, and the influence of the changed power-law distribution on the correlations. All hard works are to figure out the controlling sources of the exhibited multiscale distribution of returns. Meantime, the normalized relative structure function, the measure of fully developed turbulence, is utilized to study the general similarity and hierarchy so as to understand the special structure and mechanism of capital markets. Thirdly, the optimal volatility cascade model is constructed due to the detailed analyses of volatility transferring direction and structure property to reproduce well the multiscale behaviors, dynamics and internal structure shown in the empirical results. The cascade model is prepared for the next multiscale risk management. Finally, the cumulant of returns is calculated over different multiscale by analytic solution of moments of basic partition probability in volatility cascade model. The multiscale diversification model is therefore built to study the efficient front of assets over different timescale.The originalities of this paper are reflected in the following aspects: (1) The systematically analyses are conducted over mulitscale for capital markets including power-law distribution, criticality, power correlation, general similarity and hierarchy. (2) Three simulated series with special type of correlation are made through decomposing return to research the influence and control of certain correlation on the distributions of the multiscale returns. (3) Three measures, Granger causal test, crossed correlation function and power spectrum, are utilized to study the transferring direction and structure among the multiscale volatilities. (4) Based on the transferring direction and hierarchy of volatilities, the discrete random volatility cascade model with the more simple form of basic partition probability is built up. So the complexity of multiscale volatility is turned to the control of two key parameters of volatility cascade model. This action simplifies the difficulty of analysis greatly. (5) The cumulant of multiscale returns is expressed based on analytic solution of moments of basic partition probability in volatility cascade model. The multiscale diversification model is therefore built to study the efficient front of assets.The research makes some contributions to development of multiscale studies in capital markets. The works explore the initial fields of traditional monoscale investigations to some extend, and provide multiscale risk measure and control with some interesting ideas and methods. In addition, the relevant results also lay the foundation for the further development of theories, methods and applications in investment, decision and risk management.