Risk Analysis Of Foreign Exchange Rate Portfolio Based On Mixed Copula-SV-T Model

With the rapid development of the international financial market, the interdependence among the foreign exchange market is strengthen gradually, the dependence structure is more complex, how to measure the correlation is significant. It is generally known that there are many common characteristics about financial variables, such as rush thick tail, asymmetry, non-normal synergy and so on. Depend on the traditional linear Pearson correlation method to analyze the dependence structure among financial variables is really limited. However, the emergence of copula theory make a great contribution to the progress of the correlation research. Since the copula theory is applied to the financial field, copula function is widely used in the field of financial and insurance, such as correlation analysis, risk management, asset pricing and portfolio choice, etc. Copula become a powerful tool to solve the problem of financial correlation, and bring a new breakthrough to the financial risk measurement method.Firstly, this paper systematically introduces the definition and properties of copula function, and expounds the Sklar theorem and three kinds of correlation measurement based on copula. Then list several commonly used elliptical copula functions, Archimedean copula functions and their characteristics. Then introduced the copula function parameter estimation method, this paper chooses two step maximum likelihood estimation method to estimate copula parameter. Finally, introduced two methods of model selection:one is the traditional method AIC information method, the other one is copula information criterion which is especially suitable to copula model selection.First of all, this paper choose the euro and the pound on the yuan’s exchange rate daily yields between 2008 and 2014 as sample data, due to the spike thick tail of sequence of yield and volatility of heteroscedasticity, random fluctuation SV-t model is choose to distribute the single asset earnings volatility as marginal distribution, K-S test results show that SV-t model is appropriate to fit marginal distribution. Second, two different type of mixed copula models is built:one kind of the mixed copula models is consists of three different type of Archimede copulas, they are Gumbel copula, Clayton copula and Frank copula, then based on average model theory, established a simple mixed copula model and Smooth-AIC mixed copula model. The other one mixed copula model is composed of normal copula, based on mixed binary distribution theory. After that give a brief introduce about the estimation method of correlation coefficient and weight coefficient.In the end, different mixed copula-SV-t models is presented in this paper, after Monte Carlo simulation process of portfolio VaR value, the VaR value of the portfolio under two types mixed copula model is calculated. By the first kind of mixed copula model to structure the dependence of two kinds foreign assets, AIC test results show that Smooth-AIC mixed copula model is best fit of the related structures. Then measure the risk of investment portfolio, and under the risk minimum principle determine the best proportion of investment. By The ratio of VaR value and standard deviation of rate of return results show that the constructed two mixed copula-SV-t model is better than single copula-SV-t models on accurately assess the risk portfolio VaR value. Also, by the second kind of mixed copula model to structure the dependence of two kinds foreign assets, calculate and analysis VaR value, shows that under different confidence levels, the mixed copula models are better than single copula model on accurately assess the portfolio risk VaR value, so that we can more effectively manage the risk of a portfolio manage the risk of a portfolio.