Research And Application Of Asymptotic Method Of Financial Risk Measurement

The Basel Committee on Banking Supervision replaced VaR(Value at Risk)with ES(Expected Shortfall)as a tool for financial market risk measurement in 2012 in order to overcome the unsatisfactory consistency risk theorem existing in VaR and block diversity The shortcomings of risk and risk measurement are still one of the most active and challenging research topics in financial engineering today,so they continue to stimulate innovative methods.VaR and ES are two commonly used and important risk measures.These two quantities are not directly observable.VaR is intuitive and simple.ES is a consistent risk measure,but there are still many shortcomings in the calculation method.In most cases,There is no simple closed solution,especially the integral operation of ES,so it is necessary to study its approximate calculation and numerical solution.This article first reviews the theoretical introduction of VaR and ES and some traditional calculation methods,and summarizes the advantages and disadvantages of these methods and the application conditions.By combining Edgeworth expansion and Saddlepoint expansion of a series of approximate calculations,the asymptotic method of financial risk measurement is deeply studied under the two VaR and ES risk measurement theoretical frameworks,and the asymptotic expressions for calculating VaR and ES are proposed respectively.In many statistical problems,we do not directly use the distribution of statistics but need the quantile of the distribution.Cornish-Fisher is based on the inversion of the Edgeworth expansion to calculate the quantile.It is used for the Cornish-Fisher formula The defect problem in the method uses the moment correction skewness and kurtosis coefficient to solve the problem that the skewness and kurtosis parameters in the formula are confused with the actual skewness and kurtosis of the distribution.The simulation results show that the correction skewness and kurtosis can be used to improve the accuracy of the Cornish-Fisher calculation of VaR values,but the correction skewness and kurtosis are not suitable for Edgeworth expansion to calculate ES values,and the experimental results have no relationship with the sample size.In view of the distribution problem involved in the integration calculation of ES,the integration function of the tail is converted into the calculation of the incomplete gamma function with the help of Edgeworth’s expansion of the density function,and the quantile estimate obtained by Cornish-Fisher is brought into the calculation of the ES value.Asymptotic expression.Secondly,analyze and summarize from the perspective of Saddlepoint expansion.By reversing the Lugannani–Rice formula,the estimated value of VaR is obtained according to the moment generating function of the random variable and the cumulant generating function,and combined with the existing research results,using Saddlepoint expansion calculates the accuracy of VaR,replaces the Saddlepoint expansion of the density function and distribution function with the corresponding value in the asymptotic expression to calculate the ES value.Finally,the paper conducted a simulation calculation to compare the effectiveness of the three methods.The results showed the validity of Bootstrap as a reference value.Then,Alibaba’s stock was studied for empirical analysis.The Monte Carlo simulation results showed that the Edgeworth expansion method was used to calculate the ES More accurate than Saddlepoint expansion.