Var : A Connection ( Copula ) Application Of The Function

Ttraditional calculation method of Value at Risk of the portfolio supposes that the return rates of the financial assets should be obeyed the normal distribution, also discribes the dependence of the return rates of the financial assets with the linear correlation of Pearson. However, in practice the return rates of the financial assets obviously have the character of non-normal distribution and non-linear correlation because of sharp peak and thick tail of the distribution of the return rates.Hence,it is not rational to use the Ttraditional calculation method of Value at Risk of the portfolio. Therefore it is necessary to apply rational method in discribing the real distribution and dependence of the return rates. However, applying the Copula function, which can conjunction with any marginal distributions, we can construct a nimble multivariate distribution and obtain the real distribution and dependence of the return rates, then we can construct a more efficient risk management model.This paper mainly study the application about the Copula function in computing the Value at Risk of the potfolio. In this paper, firstly I give a simple introdution about the concept of Value at Risk and conclude the development of the calculation method of Value at Risk. And this paper gives a detailed introdution about the Copula. Also I introduce about the definitin of the tail dependence, and express it with the Copula function. Then I can apply the GARCH model in getting rid of the fluctuation and correlation, also apply the extreme value theory in anlyzing the residual error which is independente and together obeys the thick tail distribution, and fit to the marginal distribution of the Copula function with the GARCH model and the extreme value theory. And then ,on the basis of the Copula function, I can construct the joint distribution that reflects the dependence and the real distribution of the return rates about financial assets. Moreover I study the Monte Carlo simulation technique which is used to compute the Value at Risk of the potfolio. Finally, comparing to other methods, we will find that giving the amount of the investment and confidence level, the potfolio with application GARCH-GPD-Gumbel Copula model can reduce more risk of investment comparing to the investment in a index, so it shows that GARCH-GPD-Gumbel Copula model is superiority.In this paper ,there is different with other papers about computing the Value at Risk of the portfolio combining GARCH model, the extreme value theory and the Copula function.