The Question Of Estimation About Single-index Quantile Model And Application On CoVaR

VaR is the maximum loss that a single financial asset or market may suffer under a given probability level.With the 2008 outbreak of the financial crisis,people pay more attention to the importance of the measure of systemic risk,and before this crisis,for the measure of risk,people mainly concentrated in the individual financial assets to capture risk between each financial institution or the transfer market.This paper studies systemic risk in the bank system of our country,and uses the current mainstream CoVaR method to measure the risk spillover effect of systemic risk among every bank.To measure CoVaR,the linear quantile model was adopted by Adrian and Brunnermeier(2011),while the linear model is difficult to capture the real and accurate model and risk.In order to fit the real model more accurately and capture the real risk level,this paper combines single index quantile model with CoVaR to measure systematic risk.The linear structure of single index quantile model makes independent variables be explained easily,and the form of the unknown model fitting model is more flexible and close to the real model,and join in the process model in estimation of the variable selection,to filter out the relevant variable and eliminating irrelevant variables,which makes the model estimation more real and gets more useful information,the resulting estimators are consistent.The single index quantile model is a semiparametric model.At present,the estimation of semiparametric model is one of the most advanced problems in the field of statistical research.The standard form of the single index model is:Y= g(XT?)+?Among them,Y ? R is the response variable,X =(X1,...,Xp)?RP is the covariate,? is the model error,g(·)is the unknown connection function,and ? =(?1,...,?p)T?Rp is the unknown index parameter vector,in order to identify the model,???= 1 and ?1>0set up.This paper will introduce the method of iterative estimation of single index quantile model,which is based on minimizing the sum of loss function and the quantile estimation coefficient and coupling function,but because the connection function form is unknown,the estimation problem becomes complex.The method of iterative estimation procedures will be split into two steps.First,given a parameter estimation,using local linear quantile regression and Taylor expansions to estimate link function;and then according to the connection function estimation,parameters can be obtained;the two-step iteration can get accurate estimation.The complete iterative method of single index quantile estimation can obtain the asymptotic property of the estimator.Many models are sparse,in order to select significant variables,the variable selection is adopted in estimating single index quantile model,the variable selection method adopted is the adaptive LASSO,this method has been proved to have oracle property.In this paper,a single index quantile model with variable selection is simulated for data with multiple error distributions,and the simulation of the finite sample is proved.The single index quantile model is applied to Co VaR to measure the systematic risk,and the linear structure of the single index model can be applied on the basis of the linear quantile model proposed by Adrian and Brunnermeier(2011).In this paper,14 commercial banks on the Shanghai stock exchange are selected and the single index model and linear quantile model are used for the systemic risk estimation and comparison.Then introduce the backtesting,including Ljung-Box test and CaViaR test to test the performance,the test results show that the estimation of single index quantile model results will perform better a lot.Finally,the systematic risk and variable selection results are analyzed,get the conclusion that the systemic risk of bank can be estimated by the risk of single bank,the volatility and return of financial market.