The Research And Application Of VaR And CVaR Based On Stable Distribution

Right investment decision requires reliable predictions ofreturn and risk, and reliable predictions can only be obtainedif the underlying statistical model rests on realisticassumptions. Stable laws are able to capture the two maincharacteristics of empirical evidence that returns have aheavy-tailed and skewed distribution. The stable distributionsof the returns of Shanghai Stock Composite Index and ShenzhenStock Sub-index are discussed, and the VaR and CVaR under thestable distribution are further researched. The main contentsand results are as follows:1. The basic theories of univariate stable distribution andmultivariate stable distributions and stable stochasticprocesses are introduced.2. The returns of Shanghai Stock Composite Index andShenzhen Stock Sub-index are analyzed by means of normaldistribution and stable distribution simulation. Allparameters are estimated by the maximum likely estimation anddistribution simulation optimistic is measured by x~2 test andDn test. The results show that thestable distribution is fitterfor real return of Chinese stock market than normal distribution.3. The basic principle and main methods of VaR and CVaRcomputation. Value at Risk and conditional Value at Risk of thereturns of Shanghai Stock Composite Index and Shenzhen StockSub-index are computed under the stable distribution and thevalidity of VaR and CVaR is tested by back testing. The resultsshow that Yak model under stable distribution is more able tomeasure the risk of stock market and the CVaR model under stabledistribution is more able to measure the extreme risk of stockmarket than normal distribution.4. The stable GARCH model is applied to the returns ofShanghai Stock Composite Index and Shenzhen Stock Sub-index.Based on this, VaR and CVak are computed and tested. The resultsshow that VaR model under stableGARCH is more able to measurethe risk of stock market and the CVaR model understableGARCH is more able to measure the extreme risk of stockmarket than normal distribution.