The Research And Application Of Copula Functions In VaR Measurement For Portfolio

The financial market is full of risk, and there are two questions which investors have toface: the first question is whether one financial market will fluctuate violently when the othersfluctuate greatly. The second issue is when the investors hold an investing portfolio, howmuch risk do they face and how to measure the value at risk.According to the advantage at measuring the dependence between assets more efficiently,copula has great strength at the problems of dependence measure and VaR calculation. Thisessay will concentrate on the applications of copula on the issues of dependence measurebetween different financial assets and risk management of financial investing portfolio basedon VaR.The first problem to be solved is based on copula function and deriving tail dependencebetween the two financial markets, taking the CSI300Index and Hang Seng Index in HongKong’s daily return rate series as the researched object, we analysis the correlation’s changesbetween them. In the end, we evaluate the five bivariate copula model’s effectivenessaccording to rank correlation and Euclidean square distance, and make conclusions that whichone is better fit to the observational data.The second problem to be solved is to apply copula technology to the portfolio VaRmeasurement and make comparison to the traditional method. Copula function familycontains Guass-Copula, t-Copula, Clayton-Copula, Frank-Copula and Gumbel-Copula. Theresult shows that the VaR based on copula algorithm is generally greater than the traditionalone in most cases, indicating that the traditional VaR underestimates the risk. Copula functionmore fully consider the correlation between variables and not confined to the normallyassumption, so a greater degree of risk to be considered.