The Application Of Copula Method On Portfolio And Financial Risk Management

With the developing of financial market and economic globalization, there are many new problems and challenges existed in the field of financial risk management. On the one hand, the correlationship between financial assets is becoming more and more complicated, which made the traditional linear models failed in modeling their risk relationship. On the other hand, the purpose of financial risk management is not only on financial asset or portfolio selection but also on associated management of all kinds of risks in different market. Based on this background, a powerful method is required for measuring sophisticated correlation of random variables.Copula is a kind of function that is mainly used to estimate the jointly distribution of random variables. Comparing to traditional models, Copula method can characterize complicated dependent patterns between variables. This article applied Copula method on various kinds of financial risk problems and got some valuable results. Based on a systematical comparison among correlation measures, the author summarized many advantages of Copula method. The main achievements of this thesis are listed as follows:At the first part of this thesis, the author adopted Copula-GARCH model to weights calculation of currency basket portfolio. Since current weight estimation methods ignored the correlation among the currencies in the basket, which leaded to serious collinearity and insignificance problems in the model, the author used Copula model to calculate the optimal weights of currency basket that minimized the risk of portfolio. Based on this optimal weights vector one can get some information about the exchange rates policy of central bank. In our model, the"Maximization by Parts in Likelihood"method is also used to improve the precision of parameters estimation. Empirical result suggests a larger weight should be optimally accorded to the dollar in the basket of U.S. dollar, Euro, Japanese yen and Korean won, while the volatility of RMB is wider than before. This result indicated that Chinese exchange rate reform has got some positive effects.The traditional risk analysis models for one stock or portfolios mainly focus on modeling the volatility of their return. While in our thesis, the author provided a different method to model the correlationship between continuously rising and falling stock returns, which is a new angle for describing the trend of stock market. According to the character of samples, this thesis jointly used Log-ACD and Archimedean Copula for the first time and got well fitting result. At the last of this part, the conditional VaR of continuously rising and falling stock returns is computed and based on which the"Figure of Rising and Falling Risk"is proposed to analyze the trend of stock market. The empirical result showed that the conclusion of this model is consistent to real market.In our research on market risk analysis, this thesis also proposed a nonlinear time-varying method for measuring systematic risk in the stock market. The author used three kinds of GARCH models and six kinds of time-varying Copula models to fit the marginal and joint distributions of four sectors'index return in the Chinese stock market. With the best fit model, the author calculated the conditional VaR of daily returns of four sectors with a given market return level. Then two variables namedΔLCVaR andΔUCVaR were calculated for measuring the downside and upside systematic risk for each sector. Empirical test showed that our model gained an accurate result and can catch the time-varying effect of systematic risk well. Since there is no need to assume symmetric and normality of financial returns, our nonlinear model includes more risk information and can measure systematic risk more accurately than traditional beta.The final part of this thesis is mainly concerned on recognizing and measuring credit risk and its relationship with market risk for listed companies. Considering the character of high dimension and high correlation in the credit risk data set, the author firstly designed a new non-parametrical method for the variable selection. Empirical result showed that this method can not only effectively exclude the noise and collinear variables form the original data set but also help us recognize the factors of credit risk. Secondly, based on this variable selection method, the thesis modeled the relationship between credit risk and changes in market value of listed companies with kernel estimation and Copula methods. The applicability of currently structure credit risk model was also been tested under large samples.