Non-parametric Estimation Of Copula-based Risk At Values

With the constant deepening of economic globalization, financial markets relationship becomes close. Many financial crises occurred frequently recently. It is challenge for risk managers, so they need to select more suitable risk model to study these situation. In the traditional financial risk measurement model, the basic method is based on normal distribution, and then the variance-covariance method used to solve the portfolio value at risk. Although the traditional method has the advantages of simple operation, but in fact the distribution of assets price presented "a fat tail" and "extreme" does not meet assumptions of normal distribution. Meanwhile, the traditional correlation coefficient matrix can not describe the non-linear relationship between asset prices from the portfolio assets. Therefore, we need to develop new methods to measure the risk at value of an asset portfolio at risk management.In order to measure value at risk, many scholars introduce the Copula function to the study of value at risk. Copula functions can not only capture the variables of nonlinear, non-symmetrical relationship, but also they are very easy to catch the tail of the correlation between variables. This makes the Copula function more and more popular among risk managers.Most of the traditional methods of value at risk must assume a certain model firstly, such as normal distribution, but these models can not accurately describe the distribution of financial asset returns. The non-parameter estimation can fit the characteristics of the data itself better because it can't be constrained by some model, so its use is also increasing.The thesis studies the problem about the measurement of value at risk using the non-parametric estimation and Copula function. Firstly, the VaR theory, Copula theory and the theory of non-parameter estimation was reviewed. Then it analyzed the basic idea, the basic concepts and the corresponding calculations of the VaR theory, Copula theory and nonparametric estimation theory. It used non-parametric kernel density estimation to estimate the marginal distribution of Portfolio because the assumption about the marginal distribution is not accurate, and then selected the optimal distance Copula by calculating the distance between real and simulated value which is measured by Monte Carlo simulation methods based on the Copula function. It used the optimal Copula function to describe the correlation between the portfolios. Also it used Monte Carlo simulation based on the optimal Copula to measure VaR between the portfolios. Finally, the empirical research and the after test on the Chinese stock market proved the feasibility and effectiveness of the methods.