| The value at risk can be expressed as a simple and exact figure to represent the change in the rate of return of a portfolio over a period of time in the future.When calculating the return rate of securities portfolio,the return rate and other financial time series have the feature of heavy tail.This kind of problem is generally not applicable to normal distribution.In this case,we can choose the sub-exponential distribution,which is an important kind of heavy tail distribution and can effectively solve this kind of problem.This paper studies the daily closing price of Shanghai composite index.Firstly,the definition and calculation method of the value at risk are introduced.By comparing the advantages and disadvantages of historical simulation method,Monte Carlo simulation method and extreme value method,the extreme value method is selected to calculate the value at risk of daily closing price.Since the return rate of Shanghai composite index has the feature of heavy tail,the distribution family of secondary indexes is itself a heavy tail distribution,so Weibull distribution and Generalized Pareto distribution in the distribution family of sub-exponential distribution are selected as the distribution models,and the normal distribution is taken as the comparison.Then,L-moment estimation is selected to estimate the parameters in the distribution function,The population L-moment of theoretical distribution and the population L-moment of sample data are calculated,and let the population L-moment equal to the sample L-moment,so the estimated value of parameters are obtained.The PP diagram and KS test were used to test the three distributions obtained.It was found that the fitting effect of the sub-exponential distribution was better than that of the normal distribution,among which the Weibull distribution had the best fitting effect.In the end,the values at risk based on the three distributions are calculated,and the results are analyzed. |
PDF Full Text Request