The Study Of Measure Of The Market Risk Based On The Extreme Value Theory And The Copula Model

As market risk is a main financial risk in financial industry,how to measure it accurately is very necessary and meaningful.This paper uses VaR(Value-at-Risk)which is the widely used in recently research as the measurement of the market risk.Copula models and extreme value theory are effectively used to measure market risk by modeling the dependent relationship among components of a random vector and determining the joint distribution.The study in the paper is based on the influence of extreme events in financial markets and the dependent relationship among different financial assets.The Copula models and extreme value theory are used to forecast the VaR of portfolio.The study about the measurement of market risk based on extreme value theory and Copula models are represented in this paper and some empirical analysis on the VaR of the financial asset as well as the portfolio combined by different financial products is also proposed.The main work and innovations are as follows:(1)The measurement of market risk for single asset.In this part,the method based on the financial time series model and the extreme value theory is provided and applied to calculate the market risk of crude oil market and foreign exchange market.For crude oil market the day logarithm yield sequence of the price of oil in WTI is taken as an example.The purpose of this paper is to estimate tail-related risk measures including static and dynamic risk measures based on the extreme value theory.The study first estimates the static VaR by the POT model(peak over threshold model)and verifies the effectiveness and accuraacy of VaR based on this model compared with the classic variance-covariance method.As the return series in this paper are asymmetrical,skewed and fat-tailed,the skewed t-distribution with GJR-GARCH model is used to model for them firstly,then the POT model is applied to the residuals of GJR-GARCH and the dynamic VaR is calculated.In addition,the result of backtesting indicate that the method used in forecasting dynamic VaR describes the characters of the data appropriately.For the foreign exchange market,the day logarithm yield sequence of the exchange rate of USD,HKD,JPY and EUR against RMB are taken as examples.The foreign exchange returns sequence owens the properties of non-normal,sharp-peaks,heavy-tails,heteroscedasticity and so on.Based on these features,the paper fits the GARCH-type for each financial sequence under the AIC to obtain the innovation series which are independent identically distributed.To emphasize the influence of extreme events on the market risk,this paper uses the new method of tail index estimation given by Iglesias as well as the estimation method given by Hill to analyze the VaR for the foreign exchange market.And the result shows that for JPY the VaR based on new method of tail index estimation is more accurate than that based on the method of Hill estimation,but it is opposite for USD,HKD and EUR.(2)The market risk measurement of the binary portfolio.This part of the paper does some theoretical research and empirical analysis.In theoretical aspect,the paper does research on modeling binary mixture Copula functions as well as the parameter estimation and simulation of the mixture Copula functions.For marginal distributions,it applies the extreme value theory to build the model based on some research about the the above discussion in Chapter two.A semiparametric marginal distribution based on the Kernel density estimation and the peak over threshold model is proposed.And it also pointes out that the convergence and continuity of the marginal distribution function in the model.In the component dependency model,considering the disadvantages that the pure Copula models usually can not depict the dependent relationship accurately between two random variables in finance,the mixture Copula model which is based on the S-AIC criterion and the mixrture Copula model which is based on Kendall rank correlation are both provided in this paper.The method for calculating VaR of the portfolio by the mixture Copula model is also proposed.It is proved that the mixture Copula model based on S-AIC criterion is more effective than a single Copula model for calculating VaR for the portfolio constructed by the crude oil in the WTI market and Shainghai Stock Index.It suggests that the mixture Copula model based on Kendall rank correlation is effective for calculating the VaR for the portfolio constructed by Shanghai Stock Index and Shenzhen Component Index,and thus can provide some optimal portfolio just from the minimum VaR.(3)The market risk measurement for the portfolio.Considering the disadvantages of the multivariate Copula function to describe the dependent structure of multivariate variables,and to highlight the impact of extreme events on market risk,the model based on the value extreme theory and the vine-Copula structure is presented in the paper.In this part,the paper constructs a model to measure the aggregate risk of the portfolio based on the extreme value theory and vine-Copula method.Firstly,in order to highlight the impact of extreme events on the value of risk,a semiparametric marginal distribution based on the peak over threshold model is built.Secondly,the dependent relationshio among components is characterized by the R-vine-Copula model which does not need to assume the spanning the tree structure in advance.Then,the numerical algorithm steps to calculate the VaR by the above model is given.Finally,an empirical analysis is presented.The VaR forecasting results of the portfolio which is composed by five stock market index return rates in Asia under the C-vine-Copula,D-vine Copula,R-vine-Copula structure and multiple Copula models are presented in the paper.The evaluation about the advantages and disadvantages of each model through backtesting is presented.It is found that the R-vine-Copula can describe the dependence among each component most accurately and completely.In addition,the Monte Carlo simulation result for the VaR calculating under this model is also the most reliable.These conclusions can provide investors some investment advice.