A Varying-Coefficient Expectile Model for Estimating Value at Risk

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)576-592
Journal / PublicationJournal of Business and Economic Statistics
Issue number4
Online published28 Oct 2014
Publication statusPublished - Oct 2014


This article develops a nonparametric varying-coefficient approach for modeling the expectile-based value at risk (EVaR). EVaR has an advantage over the conventional quantile-based VaR (QVaR) of being more sensitive to the magnitude of extreme losses. EVaR can also be used for calculating QVaR and expected shortfall (ES) by exploiting the one-to-one mapping from expectiles to quantiles, and the relationship between VaR and ES. Previous studies on conditional EVaR estimation only considered parametric autoregressive model set-ups, which account for the stochastic dynamics of asset returns but ignore other exogenous economic and investment related factors. Our approach overcomes this drawback and allows expectiles to be modeled directly using covariates that may be exogenous or lagged dependent in a flexible way. Risk factors associated with profits and losses can then be identified via the expectile regression at different levels of prudentiality. We develop a local linear smoothing technique for estimating the coefficient functions within an asymmetric least squares minimization set-up, and establish the consistency and asymptotic normality of the resultant estimator. To save computing time, we propose to use a one-step weighted local least squares procedure to compute the estimates. Our simulation results show that the computing advantage afforded by this one-step procedure over full iteration is not compromised by a deterioration in estimation accuracy. Real data examples are used to illustrate our method. Supplementary materials for this article are available online.

Research Area(s)

  • Asymmetric squared error loss, Expected shortfall, Local linear smoothing, One-step weighted least squares, Value at risk, α-mixing

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