Research on Semiparametric Asymmetric Joint Elicitable Risk Model Based on the Laplace Distribution
In recent years,due to the superior performance of semiparametric joint elicitable risk models in joint statistical modeling and prediction of value at risk(VaR)and expected shortfall(ES),they have attracted widespread attention in the field of financial measurement.This paper first studies the statistical properties and risk prediction performance of the model under the framework of the asymmetric Laplace distribution.Unlike the existing semiparametric joint elicitable risk models,this model jointly models VaR and ES by assuming the conditional distribution of asset returns follows the asymmetric Laplace distribution based on VaR and ES,taking into account the typical asymmetric characteristic of financial markets,and regarding VaR and ES as dynamic structures composed of conditional standard deviation process of returns containing the asymmetric feature and a parameter to be estimated.Based on the structure of the model,we discuss the quasi-maximum likelihood estimation method and establish the consistency and asymptotic normality theorems for the estimator under certain regular conditions.Subsequently,numerical simulation results considering various conditions confirm the finite sample properties of the estimator and the effectiveness on predicting one-step ahead risks.Finally,empirical results show that the proposed model performs best in predicting multi-step ahead VaR and ES.
Value at riskexpected shortfallsemiparametric asymmetric joint elic-itable risk modelasymmetric Laplace distributionasymptotic property
NETL
NSTL
万方数据
