Application Of Pair - Copula Method In Fund Risk Measurement

Faced with the complexity of the financial market, it is more necessary to manage the risk of fund portfolios, especially the social security fund portflolio. Now, the thecoretical and empirical study of a single asset is well-developed, which means models like GARCH, SV and extreme valve theory(EVT) can be used to describe the distribution of the return rate of an asset. However, when it comes to a portfolio, it has been proofed that the liner model is not appropriate to describe the correlations between different financial assets.Recently, a method named “Copula” attracts the researchers’ attention. Because the copula does not require the same shape of marginal distribution and allows the non-linear and asymmetrical dependence between assets, it gives some insight to understand the portfolio. But, the copula is still not perfect, which limits its application in risk control field. It requires that the branch connection fuctions should have the same type. Also, the copula could not solve the problem coused by extreme value.This paper tries to establish a Pair-Copula-GARCH-GPD model, in which both the EVT and the Copula Theory are used, to measure the VaR more accurately. Specifically, on the base of traditional GARCH-Copula model, the Vine structure and Pair-Copula method are introduced to establish a Pair-Copula-GARCH model. In this new model, the same type limits of the branch connection functions are not required. So more flexible models can be made. Then, the distribution is divided into two parts – tail part and middle part. The EVT is used to describe the tail parts and the kernel estimation is used fit the middle part. All these improvements make the new model break through the harsh assumption of traditional approach, which can be used in fields with great limitations and high level of risk management.To assess the practical performance of the Pair-Copula-GARCH-GPD model, the VaR of No.503 portfolio of social security fund is calculated with Monte Carlo simulation. Compared with some popular models like GARCH-Copula model, variance-covariance approach and history simulation, the empirical result and loopback test show that the PairCopula-GARCH-GPD model has the best goodness of fit and is more flexible.Further research can be conducted in four aspects in the future, which includes the richness of the Vine structure, the diversity of marginal distribution, the degree of EVT’s application and the dynamic condition of Pair-Copula model.