Generalized Method Of Moments Theory Based On Simulation And Its Application In Integrated Risk Management

Method of moments estimation is a commonly used,simple and effective parameter estimation method.This method is a method which uses the sample moments and functions satisfying the sample moments to estimate the corresponding population moments.Method of moments estimation does not require the type of a general distribution.On the basis of the method of moments estimation,Hansen proposed a generalized method of moments estimation that is equally effective for over-identification tests.This method requires that the parameters to be estimated meet some moment conditions,and it is the extension of the classical method of moments estimation.Although the generalized method of moments estimation has many advantages,it is suitable for large sample cases,which is similar to the classical method of moments estimation.When the sample data is small,the generalized method of moments estimation can not effectively estimate the parameters.At this time,the improved generalized method of moments estimation based on simulation can be used to estimate the parameters.The theory shows that under certain conditions,the simulation generalized method of moments estimator has consistency and asymptotic normality.The simulated generalized method of moments estimation can solve the problem of the error caused by the lack of data.Operational risk loss events bring a lot of hidden dangers to the financial industry.Under normal circumstances,although the frequency of the operational risk loss event is low,the loss is very large,that is,operational risk has a "low frequency high loss" feature.While the data of operational risk loss is less,and the loss distribution function of various operational risks is different,it is difficult to directly fit the joint distribution function of the operational risk loss with the common distribution function.Efron's Bootstrap repeated sampling method has helped to solve the problem of operational risk data.Use Bootstrap repeated sampling method to extract the original data as a new sample data,and then process and analyze for the new sample data according to the need.The emergence and use of Copula functions solves the problem of joint distribution function fitting for operational risk loss.In analyzing the joint distribution function of operational risk loss,we can choose the appropriate variety of Copula functions and marginal distribution functions to construct various joint distribution functions which we need.When constructing the joint distribution function using Copula function,we need to estimate the parameters of Copula function.At this time,we can estimate the parameters according to the simulated generalized method of moments estimation.After estimating the parameters of the Copula function,the Monte Carlo simulation is used to calculate the loss of operational risk.The empirical analysis shows that the simulation generalized method of moments estimation can effectively estimate the parameters of Copula function;Regardless of the correlation between the various operational risks,it will overestimate the risk when the operational risk is estimated simply by summing up the loss of various operational risks as a total loss;It is effective to use the Copula function to estimate the loss of operational risk.