| Since 1980s, economic globalization brings to an important change for the world’s financial system:the local financial turmoil in a country or region will spread to financial markets of other countries at a very fast speed. That led to huge fluctuation of asset prices in the world wide. This phenomenon is namely "financial contagion". In the background of globalization, the measurement of financial contagion is significant for policy formulation of governments and portfolio allocation in world wide of big fund. However, there are many obvious defects in mainstream of the finance theory. Therefore, we are from a new perspective of complex science to study financial contagion based on fractal market hypothesis. First, in order to exclude the interference of individual market to contagion, fractal market analysis mothod is used to filter the conditional volatility for each markets. Second, we propose a qualitative method based on dynamic copula to measure the strength of contagion, and then use the results to optimize the portfolio. We expect our study can able to provide useful suggestion for financial regulatory sectors of our country and investors.Firstly, we propose a new method to study financial conatagion:Copula-MFV. Based on this method, we test fianacial crisis happened in 2007 whether exist contagion to Chinese stock market. Mulitfractal volatily (MFV) is computed by using mulitfractal spectrum analysis, then standardized returns obtained. A series statistical tests show that MFV has the best performance among other methods, it provides empirical support for the next studies. The dependence structure and its variation between U.S. and Chinese stock markets are researched by using various static and dynamic copula. After above work, we test whether tail dependence obviously increased after financial crisis. The results show that the tail dependence between the two markets significant increase after financial crisis, that indicates there is exist financial crisis.Secondly, based on the qualitative test results, the quantitative measurement is carried out. Only the lower tail dependence is the key issue in financial risk management, so we then study the lower tail dependence between U.S. and Chinese stock markets. To avoid the subjectivity and arbitrariness when we choose the period of crisis and non-crisis, markov regime switching model is used to describe the variation of lower tail Kendall’s τ so as to select crisis and non-crisis exactly. The statistical characteristics of Kendall’s τ during crisis and non-crisis periods are obviously different. Generally speaking, time-varying lower Kendall’s τ in the crisis period is 1.87 times that of non-crisis on average, indicating that the contagion effect increased about 87.39% on average during crisis period.At last, we try to optimize the portfolio use above results. First, refer to the hedging model of future market, make to minimum the variance of portfolio as the optimization goal, to optimize the allocation of two assets; second, extend from two to multiple assets allocation, and under the principle of utility maximization to optimize portfolio. The empirical results show that the new method which combine the nonlinear MFV and Copula theory has a better performance in portfolio optimization.
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