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Nonparametric inference of expectile-based value-at-risk for financial time series with application to risk assessment

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  • Zhang, Feipeng
  • Xu, Yixiong
  • Fan, Caiyun

Abstract

Expectile-based value-at-risk (EVaR) is a more sensitive measure of the magnitude of extreme losses compared to the conventional quantile-based value-at-risk (VaR). Besides, EVaR is shown to be the only law-invariant, coherent, elicitable risk measure. For these reasons and other advantages, comparing with the existing risk measures (e.g., VaR and ES), EVaR has been recently recommended to use in financial risk management. This article considers nonparametric estimation of EVaR and associated statistical inference for dependent financial time series. The asymptotic properties (strong consistency and weak convergence) of the proposed estimator are investigated in the context of dependence. Monte Carlo simulation studies show that the proposed estimator has desirable finite sample performance. An empirical application to evaluate EVaR of S&P500 returns provides valuable insights for risk assessment in out-of-sample prediction.

Suggested Citation

  • Zhang, Feipeng & Xu, Yixiong & Fan, Caiyun, 2023. "Nonparametric inference of expectile-based value-at-risk for financial time series with application to risk assessment," International Review of Financial Analysis, Elsevier, vol. 90(C).
    • Handle: RePEc:eee:finana:v:90:y:2023:i:c:s105752192300368x
    DOI: 10.1016/j.irfa.2023.102852
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    1. Kuan, Chung-Ming & Yeh, Jin-Huei & Hsu, Yu-Chin, 2009. "Assessing value at risk with CARE, the Conditional Autoregressive Expectile models," Journal of Econometrics, Elsevier, vol. 150(2), pages 261-270, June.
    2. Kim, Minjo & Lee, Sangyeol, 2016. "Nonlinear expectile regression with application to Value-at-Risk and expected shortfall estimation," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 1-19.
    3. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
    4. Fang, Zheng & Li, Qi & Yan, Karen X., 2023. "A Simple Nonparametric Approach For Estimation And Inference Of Conditional Quantile Functions," Econometric Theory, Cambridge University Press, vol. 39(2), pages 290-320, April.
    5. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, September.
    6. Yao, Qiwei & Tong, Howell, 1996. "Asymmetric least squares regression estimation: a nonparametric approach," LSE Research Online Documents on Economics 19423, London School of Economics and Political Science, LSE Library.
    7. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    8. Zaevski, Tsvetelin S. & Nedeltchev, Dragomir C., 2023. "From BASEL III to BASEL IV and beyond: Expected shortfall and expectile risk measures," International Review of Financial Analysis, Elsevier, vol. 87(C).
    9. Anthony C. Davison & Simone A. Padoan & Gilles Stupfler, 2023. "Tail Risk Inference via Expectiles in Heavy-Tailed Time Series," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(3), pages 876-889, July.
    10. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(1), pages 17-39, February.
    11. 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.
    12. De Rossi, Giuliano & Harvey, Andrew, 2009. "Quantiles, expectiles and splines," Journal of Econometrics, Elsevier, vol. 152(2), pages 179-185, October.
    13. Fan, Yanqin & Liu, Ruixuan, 2016. "A direct approach to inference in nonparametric and semiparametric quantile models," Journal of Econometrics, Elsevier, vol. 191(1), pages 196-216.
    14. Fabio Busetti & Michele Caivano & Davide Delle Monache, 2021. "Domestic and Global Determinants of Inflation: Evidence from Expectile Regression," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(4), pages 982-1001, August.
    15. Johanna F. Ziegel, 2016. "Coherence And Elicitability," Mathematical Finance, Wiley Blackwell, vol. 26(4), pages 901-918, October.
    16. Song Xi Chen, 2005. "Nonparametric Inference of Value-at-Risk for Dependent Financial Returns," Journal of Financial Econometrics, Oxford University Press, vol. 3(2), pages 227-255.
    17. Fabio Bellini & Valeria Bignozzi, 2015. "On elicitable risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 15(5), pages 725-733, May.
    18. Rong Jiang & Xueping Hu & Keming Yu, 2022. "Single-Index Expectile Models for Estimating Conditional Value at Risk and Expected Shortfall [Coherent Measures of Risk]," Journal of Financial Econometrics, Oxford University Press, vol. 20(2), pages 345-366.
    19. Fabio Bellini & Bernhard Klar & Alfred Müller, 2018. "Expectiles, Omega Ratios and Stochastic Ordering," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 855-873, September.
    20. Bellini, Fabio & Klar, Bernhard & Müller, Alfred & Rosazza Gianin, Emanuela, 2014. "Generalized quantiles as risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 41-48.
    21. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    22. Kato, Kengo, 2009. "Asymptotics for argmin processes: Convexity arguments," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1816-1829, September.
    23. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    24. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    25. James W. Taylor, 2008. "Estimating Value at Risk and Expected Shortfall Using Expectiles," Journal of Financial Econometrics, Oxford University Press, vol. 6(2), pages 231-252, Spring.
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