Copula-based Methods Of Portfolio VaR Metrics Research

Risk management in recent years has experienced a real revolution, which began in Value-at-Risk (VaR). VaR is a measure of risk in financial markets in order to respond to the 20th century and early 90's developed financial disaster. Now, VaR methodology has been extended and applied to derivatives, and in general to deal with financial institutions has changed the way financial risks. With in-depth study and found that the traditional model are based on the normal use of the variance–covariance method to solve the risk of the portfolio value, the larger the difference with the actual situation, the traditional correlation coefficient matrix can not be expressed better portfolio of non-linear relationship between. Therefore, the need to develop new methods to better study the risk of the portfolio value and relevance.In recent years, Copula technology to solve these problems, provided a good idea and methods of analysis of the financial risks to a new stage. Copula function describes the correlation structure of random variables is the structure dependent joint distribution of multiple random variables a powerful tool. Random variables will be multi-dimensional construct the joint distribution of independent and split the edge into the edge of the distribution of the estimates and the correlation between the distribution of structural analysis, making the question of the structure of the joint distribution easier and more accurate. Copula function based on stochastic simulation, taking into account the dependency structure of random variables effectively avoids the difficulty settings Copula model, is superior to ignore the dependency structure of the simulation.Copula paper studied the theory of value at risk in the portfolio of applications. VaR first theoretical papers, Copula theory of a more systematic summary of the theoretical study of the status quo VaR method, including the basic principles, advantages and disadvantages, detailed calculation steps, as well as the status of Copula Theory, Copula function classification, nature, relevance of parameter estimation methods are reviewed. In the above theoretical analysis, based on the thesis for the portfolio value at risk VaR calculation as well as the relevant measure of the model exists in the problem set, the application functions based on Monte Carlo simulation of Copula methods, refer to the Shenzhen A and Shenzhen B per day trading day's closing price on the two stock portfolio value at risk measure of empirical analysis done; the use of R software random number generated, simulated data to calculate the marginal distribution for the t-Copula distribution, Copula-dependent structure function, respectively, from normal copula, t-copula, Gumbel copula, Clayton copula and Frank copula, commonly used to obtain dependency structure than in the past from normal copula and t-copula method is more accurate VaR value, and effectively control the risks. Finally, the paper also pointed out that a number of applications Copula Function the inadequacy of the theory, after all, it is still relatively short development time, while in the application of the need to constantly improve their theoretical system.