The Research On Nonlinear Dynamical Characteristics And Risk Management In The Capital Markets

The capital market and risk management is a key topic worldwide. The nature and behavior of stock market prices have been and continue to be of interest to academicians, market regulators and practitioners. Academicians have spent large amounts of both time and resources attempting to understand the behavior of security prices over time. Regulations are surely interested in the efficiency of the capital market whereas, practitioners and investor will be interested in any patterns in asset prices that are exploitable. Until recently, most of the studies in capital market have utilized linear analysis methodology under conventional Capital Market Theory (CMT). In the world of CMT, investors are assumed to be rational; the securities market is informationally efficient. Market prices reflect all public information available, so all prices are "fair". Consequently, security returns (price change) follow a random walk, volatility in financial market is the result of exogenous stochastic events ( "white noise" ).However, the linear methodology of CMT has limitations inherently as they are invalid to capture complicated "patterns" in stock prices, not to mention the crash of 1987 in U.S. stock market, which is a catastrophic phenomenon. So, a new research trend, from the point of nonlinearity and evolution instead of in a linear and equilibrium view, emerges. On the other hand, butterfly effect, Noah effect, fat tails in returns distribution and autocorrelation in financial time series show clearly that markets exhibit nonlinear dynamical characteristics. Researchers and risk managers can gain a new perspective by examining nonlinear dynamical process in capital market. This paper engages a comprehensive research from this new view.Firstly, this paper investigates the behavior of stock market prices thoroughly. The research results indicate that normality, random walk and independence (hypothesizes under the Efficient Market Theory) do not reflect the reality precisely. However, given the Fractal Market Hypothesis, non-normality, fractional Brownian Motion and long-memory can constitute the best possible approximation of the price behavior. In capital market, time series follow a biased random process, and exhibit fractal characteristic and long-memory effect. Furthermore, our empirical studies show that capital markets possess an underlying low-dimensional chaotic system. The positive Lyapunov exponents and fractional dimension (D=2.55) provide this evidence. It comes to the conclusion that the instability and volatility in capital market is the results of a deterministic process instead of exogenous impact.Based on the inherent nature of capital market as part of virtual economy, this paper presents the Nonlinear Dynamical Analysis Principle (called NDAP) to study capital market systemically, then put forwards integration rule, endogenous rule and process rule to guard risk management process. In the view of NDAP, this paper examines where financial risk comes from and how risk is generated in capital market. It concludes the nonlinear dynamics of financial time series are the result of positive feedbacks and interactions between heterogeneous investors. Moreover, in my article, a nonlinear innovative framework is provided to guide risk management in capital market, which embraces risk assessment, risk measures and risk controlling.In the end, this paper presents an integrated nonlinear study framework of capital market theory. The nonlinear system is intimately related to the fractal market hypothesis, irrational trader and biased random walk. This framework differs from the traditional linear point corresponding to the Efficient Market Hypothesis. It's convincing. that the innovative framework will give deep insight into research on financial market theory and risk management.