The Research On The Estimation Of Value-at-Risk Of Portfolio Based On Copula Function

In resent years, many well-known financial Institutions such as the Daiwa Bank, the Bahrain Bank, though sophisticated in administration, all suffered great loss as to the extent of collapse, due to inadequate administration or monitor. All this adds to the fact that with the acceleration of global finance integration and the innovation and development of the derivative financial instruments, while we are strengthening the diversification, specialization and scientificalization of financial services, the volatility and concealment of risks are also increased. So, how to accurately measure financial risks, establish perfect risk warning systems and mechanisms, has become a hot issue of financial institutions and regulatory authorities.The VaR (Value at risk) model, developed by the J P Morgan Group, due to its simplicity, efficiency and capacity to measure the integrated risks of financial institutions, has got widespread application.The application of copula theory in the financial sector happened just a few years ago. It describes the dependence of random variables. Research shows that it meets the real financial market when using the copula theory to describe risk dependences. Copula is a theory which uses sample data and marginal distributions of the returns'ratio to determine the joint distribution of the portfolio's return, it is one of the tools that are mostly used in both the construction of joint distributions and the analysis of the dependence between random variables. Based on the statistical analysis, the VaR model, as a risk measure technique, has a core issue which lies in the description of the statistical distribution or the probabilistic density of financial time series. So, it comes in handy when using the copula theory to study VaR.This paper showed the definition and the main calculation methods of VaR and then briefly introduced the related theories of copula, and using the copula theory, this paper deduced the probabilistic density of portfolio's return ratio. At last, this paper gives the solution of VaR based on both the Monte Carlo simulation method and the integral transformation method. In the past, most empirical literature adopted a normal or lognormal assumption on return's ratio; however, it turned out to be not the case. The statistical characteristics of some financial assets'indicator are peak and fat tail, not normal. This paper intended to establish a model or method to overcome the normal restrictions. This paper established the random variables'joint distribution and probabilistic density which can reflect their dependence. The result is theoretically significant and overcomes the difficulty when describing the joint distributions of returns'ratio. Meanwhile, this paper gives the solution of VaR based on both the Monte Carlo simulation method and the integral transformation method and makes it possible to calculate the risks of portfolios according to some real distributions. This method could reflect time-varying relevance and volatility of returns'ratio.