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A Varying-Coefficient Expectile Model for Estimating Value at Risk

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  • Shangyu Xie
  • Yong Zhou
  • Alan T. K. Wan

Abstract

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.

Suggested Citation

  • Shangyu Xie & Yong Zhou & Alan T. K. Wan, 2014. "A Varying-Coefficient Expectile Model for Estimating Value at Risk," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 576-592, October.
    • Handle: RePEc:taf:jnlbes:v:32:y:2014:i:4:p:576-592
    DOI: 10.1080/07350015.2014.917979
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    Cited by:

    1. Xiu Xu & Andrija Mihoci & Wolfgang Karl Hardle, 2020. "lCARE -- localizing Conditional AutoRegressive Expectiles," Papers 2009.13215, arXiv.org.
    2. Yundong Tu & Siwei Wang, 2023. "Variable Screening and Model Averaging for Expectile Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(3), pages 574-598, June.
    3. Tu, Yundong & Wang, Siwei, 2020. "Jackknife model averaging for expectile regressions in increasing dimension," Economics Letters, Elsevier, vol. 197(C).
    4. Tae-Hwy Lee & Aman Ullah & He Wang, 2019. "The Second-Order Asymptotic Properties of Asymmetric Least Squares Estimation," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 201-233, September.
    5. Xu, Xiu & Mihoci, Andrija & Härdle, Wolfgang Karl, 2018. "lCARE - localizing conditional autoregressive expectiles," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 198-220.
    6. Yao, Yinhong & Li, Jianping & Sun, Xiaolei, 2021. "Measuring the risk of Chinese Fintech industry: evidence from the stock index," Finance Research Letters, Elsevier, vol. 39(C).
    7. Zongwu Cai & Ying Fang & Dingshi Tian, 2018. "Assessing Tail Risk Using Expectile Regressions with Partially Varying Coefficients," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201804, University of Kansas, Department of Economics, revised Oct 2018.
    8. Alan T. K. Wan & Shangyu Xie & Yong Zhou, 2017. "A varying coefficient approach to estimating hedonic housing price functions and their quantiles," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(11), pages 1979-1999, August.
    9. Zhang, Feipeng & Li, Qunhua, 2017. "A continuous threshold expectile model," Computational Statistics & Data Analysis, Elsevier, vol. 116(C), pages 49-66.
    10. Man Wang & Kun Chen & Qin Luo & Chao Cheng, 2018. "Multi-Step Inflation Prediction with Functional Coefficient Autoregressive Model," Sustainability, MDPI, vol. 10(6), pages 1-16, May.
    11. Marcelo Brutti Righi & Fernanda Maria Muller & Marlon Ruoso Moresco, 2022. "A risk measurement approach from risk-averse stochastic optimization of score functions," Papers 2208.14809, arXiv.org, revised May 2023.

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