The Volatility Spillovers And Dynamics In Stock Network From Time-frequency Perspective

The prevention and control of financial volatility risk has been testing the wisdom of market participants and regulators.Understanding and describing the law of financial market volatility contagion accurately is conducive to market participants and regulators to capture market information,optimize asset allocation,formulate management policies,prevent and resolve financial crises.In order to characterize the time-frequency spread mechanism of volatility in the stock market system,this paper reveals the spread law of volatility risk in the financial network from the perspective of spillover effect between financial markets.Based on the advantages of interdisciplinary,this paper applies multi-scale wavelet analysis,complex network theory,econometrics and dynamic propagation model synthetically to analyze the volatility spillover effect and its propagation dynamics mechanism in the stock market from the perspective of time-frequency domain.The main work and innovative are as follows:(1)In order to solve the systemic problem of volatility spillover in stock market,a systematic analysis method,volatility spillover complex network,is proposed.In the spillover network model of stock market,the nodes are the stock markets and the edges are the spillover effects which are captured by the econometric GARCH-BEKK models.Empirical studies on the evolution of systematic topological characteristics of spillover networks are carried out in time domain and frequency domain,respectively.The results in time domain analysis show that,the status of most countries in spillover networks is changing frequently,but the ranking of the two extremes of volatility spillover is basically stable.Generally,the stock markets of developed countries have spillover effects on regions in developing countries where the financial markets are not sound.The frequency domain results show that the spillover relationship in the network increases gradually from short-term to long-term,but the weight of spillover effect decreases gradually.The spillover effect mainly occurs in the short-term,while there are many weak links in the long-term.In addition,spillover effects are unevenly distributed in cross-term networks.Most of the spillover relationships occur from the relative long-term to the short-term,the volatility in long-term of the markets will have a greater impact on the short-term markets.(2)To study the dynamic transmission problem in spillover network of stock market,a dynamic model is constructed based on the traditional dynamics model.In the process of studying the dynamics of complex networks,it is found that the traditional models mainly focus on the diffusion mechanism of viruses and rumors in networks.However,the degree of the impact on the disseminators is very deficient.In the stock network,the magnitude of the impact is particularly important.So,a dynamic propagation model with continuous state is constructed according to the characteristics of the spillover network.The first step of in building the model is define the changes of stock index subject in the process of dissemination.Then,the dissemination mechanism and diffusion rules between subjects are described,and the termination conditions are defined.Finally,the dynamic equations of the dissemination model are obtained.In addition,the density of spillover network in stock market is large,spillover relationship is complex.A minimal tree graph extraction algorithm for spillover networks is designed to eliminate redundant weak connection information and extract the main topological structure of the networks.(3)In order to reveal the dynamic propagation mechanism in spillover networks,an empirical study on multi-scale periodicity was conducted.The range,speed,path and degree on path of volatility transmission can be expressed by several indicators of complex network.The results show that the propagation speed and the fluctuation size will reach the peak in the second to third steps in the process of volaitlity propagation.The propagation attribute index of nodes is used to describe the role of nodes in the process of volatility propagation.Different volatility sources are selected to simulate the characteristics of volatility propagation under random attacks and key attacks through scenario setting.The proposed dynamic propagation model is applied to multi-scale networks to compare the volatility spillovers between stock index under different terms.Taking the three major U.S.stock indexes and China's Shanghai Stock Index as examples,this paper also studies the system response mechanism under the impact of volatility and explores the changes of volatility risk in the key nodes and key transmission path.