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Fractal Market Theoryand Persistence In Financial Volatility

Posted on:2004-06-09Degree:DoctorType:Dissertation
Country:ChinaCandidate:Z FanFull Text:PDF
GTID:1116360092480613Subject:Management Science and Engineering
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This dissertation studies the efficiency, volatility and persistence of financial markets. After the revision of Efficient Market Theory(EMT), we establish the Fractal Market Theory(FMT) framework, and go on with the research on several issues based on the nonlinear and fractal characteristics of financial markets: nonlinear cointegration modeling; capital assets pricing in fractal markets; persistence of financial volatility and multivariate GARCH modeling; volatility of VaR and modeling research; et al. The main work and innovations of the dissertation include:1 The dissertation analyzes the limitations of the Efficient Market Theory, and establishes the Fractal Market Theory framework by introducing the random fractal theory into the study on the efficiency and fundamental characteristics of financial markets. We give full explanations on the inherent mechanism, basic behaviors, and economic meanings of fractal markets. The signification of Fractal Market Theory and its relationship with Efficient Market Theory is clarified. The popularity of fractal markets is proved after demonstrations on three disparate financial time series.2 Estimating the nonlinear cointegration function is the key issue in nonlinear cointegration research. Wavelet neural network is introduced into the nonlinear cointegration modeling, and the modeling method is presented. The experiments of Shanghai and Shenzhen stock markets show that the performance of wavelet neural network is more satisfactory than that of BP neural network in the estimation of nonlinear cointegration function. The experiments results also indicate that there's nonlinear cointegrated relationship between two markets.3 Owing to the theoretical foundations on Efficient Market Theory, CAPM and APT are not robust in fractal markets. The dissertation gives out the assets pricing theory in fractal markets by utilizing nonlinear cointegration theory, and sets up wavelet neural network models for capital assets pricing in fractal markets. The experiment of Shanghai stock market shows that the pricing method we present above is superior to CAPM.4 The dissertation studies the market mechanism of persistence in financial volatility by investigating the market information and its influences on market volatility. The discussion broadens the connotation of Fractal Market Theory. Considering that the optimization algorithm based on gradient information is powerless in multivariate GARCH modeling, we use genetic algorithm to optimize the likelihood function of multivariate GARCH model. The calculation results of Shanghai and Shenzhen stock markets testify the volatility persistence and bivariate GARCH effect in these twomarkets, and non-copersistence between two markets is demonstrated afterwards.5 Based on Fractal Market Theory and nonlinear transformation theory of time series, we demonstrate the feasibilities and theoretical basis for the study of volatility persistence in VaR. The dissertation demonstrates at first that it is inappropriate to analyze the volatility character of VaR by modeling series, and it is appropriate by modeling series. After that, FITSGARCH model is presented, and by employing the impulse response function we define the volatility persistence in VaR. The demonstration of Shanghai and Shenzhen stock markets prove the volatility persistence in VaR in two markets.The research is sponsored by National Natural Science Foundation of China: Persistence in Volatility of Multivariate Time Series and Its Applications in Financial System (No. 70171001).
Keywords/Search Tags:: Efficiency of financial markets, Fractal Market Theory (FMT), Nonlinear cointegration modeling, Pricing of capital assets, Persistence in financial volatility, Multivariate GARCH modeling, Volatility persistence in VaR
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