Research On Returns Distribution And Value-at-risk Forecasting Based On Cornish-Fisher Expansion

As financial practice research continues to deepen,a large number of research results prove that the distribution of financial asset return series does not satisfy the assumption of normal distribution in traditional models,and shows obvious spikes and thick tails and asymmetry characteristics,and the more high frequency data shows the more obvious deviation characteristics.The three core issues of traditional finance theory-asset pricing,volatility modeling and risk measurement-are closely related to the form of return distribution,therefore,how to accurately characterize the nonnormality of risk distribution is an urgent problem to be solved.In recent years,scholars have proposed many non-normal return distribution assumptions,such as t(d)distribution and skewed t distribution,and proposed ARCH models and GARCH family models to portray the conditional heteroskedasticity of return series.However,all of these methods suffer from certain estimation accuracy shortcomings.The quantile approximation method of Cornish-Fisher expansion is one of the representative methods.The C-F expansion model can be applied to random samples with unknown distribution,and the method can directly output the quantile estimates at a given probability level using only the sample information,which is easy to calculate and the estimated quantile has high accuracy.In terms of application,valueat-risk estimation is an important indicator that investors pay attention to when conducting risk assessment of investment portfolios,and the validity of its estimation largely depends on the model setting of the return distribution.The C-F expansion method also has a wide scope of application in the field of asset risk measurement.In this paper,we study the quantile approximation method of the unknown distribution of Cornish-Fisher expansion from two aspects: model construction and model application.From the perspective of model construction,this paper establishes the quantile approximation model based on Cornish-Fisher expansion by using the information of higher-order moments(third-order moments and fourth-order moments),gives the detailed derivation process of the quantile estimation model of C-F expansion and the specific steps for calculating the estimated values,and uses the resampling simulation experiment method to perform the quantile estimation of the daily return distribution of CSI 300 stocks.The model is applied based on C In terms of model application,this paper applies the quantile asymptotic estimation method based on Cornish-Fisher expansion to the field of risk measurement,and constructs a CF-Va R model to estimate and forecast the value-at-risk index.Specifically,firstly,the idea and model form of CF-Va R model construction without realized volatility are introduced in detail,and the methods of constructing realized volatility and conditional realized volatility measures based on high frequency data are given,and conditional realized volatility is introduced into the CF-Va R estimation model construction.On this basis,an empirical study is conducted on the 5-minute return high-frequency data of the CSI300 index for a total of 127 trading days from June 16,2021 to December 17,2021,and the value-at-risk estimates are calculated and back-tested to prove the accuracy of CF-Va R model prediction.The results of this paper demonstrate that :for financial asset return series,the asymptotic quantile and Va R estimates calculated by the CornishFisher expansion model are more valid than those of the EGARCH model based on the assumption of a normal distribution.