IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i12p1961-d1678875.html
   My bibliography  Save this article

Nonparametric Estimation of Dynamic Value-at-Risk: Multifunctional GARCH Model Case

Author

Listed:
  • Zouaoui Chikr-Elmezouar

    (Department of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi Arabia)

  • Ali Laksaci

    (Department of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi Arabia)

  • Ibrahim M. Almanjahie

    (Department of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi Arabia)

  • Fatimah Alshahrani

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

Abstract

Value-at-Risk (VaR) estimation using the GARCH model is an important topic in financial data analysis. It allows for an increase in the accuracy of risk assessment by controlling time-varying volatility. In this paper, we enhance this feature by exploring the functional path of the financial data. More precisely, we study the nonparametric estimation of the multi-functional VaR function using the local linear method, construct an estimator, and establish its stochastic consistency. The derived asymptotic result provides a rigorous mathematical foundation that permits boosting the use of the VaR function in financial data analysis. Furthermore, an empirical analysis is performed in order to examine the efficiency of the proposed algorithm. Additionally, a real data application is created to highlight the multi-functionality of the VaR estimation for multi-asset risk management.

Suggested Citation

  • Zouaoui Chikr-Elmezouar & Ali Laksaci & Ibrahim M. Almanjahie & Fatimah Alshahrani, 2025. "Nonparametric Estimation of Dynamic Value-at-Risk: Multifunctional GARCH Model Case," Mathematics, MDPI, vol. 13(12), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:12:p:1961-:d:1678875
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/12/1961/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/12/1961/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Herrera, Rodrigo & Schipp, Bernhard, 2013. "Value at risk forecasts by extreme value models in a conditional duration framework," Journal of Empirical Finance, Elsevier, vol. 23(C), pages 33-47.
    2. Marius Lux & Wolfgang Karl Härdle & Stefan Lessmann, 2020. "Data driven value-at-risk forecasting using a SVR-GARCH-KDE hybrid," Computational Statistics, Springer, vol. 35(3), pages 947-981, September.
    3. K. Benhenni & F. Ferraty & M. Rachdi & P. Vieu, 2007. "Local smoothing regression with functional data," Computational Statistics, Springer, vol. 22(3), pages 353-369, September.
    4. Hao Sun & Bo Yu, 2020. "Volatility asymmetry in functional threshold GARCH model," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(1), pages 95-109, January.
    5. Cerovecki, Clément & Francq, Christian & Hörmann, Siegfried & Zakoïan, Jean-Michel, 2019. "Functional GARCH models: The quasi-likelihood approach and its applications," Journal of Econometrics, Elsevier, vol. 209(2), pages 353-375.
    6. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    7. Frédéric Ferraty & Alejandro Quintela-Del-Río, 2016. "Conditional VAR and Expected Shortfall: A New Functional Approach," Econometric Reviews, Taylor & Francis Journals, vol. 35(2), pages 263-292, February.
    8. Nour-Eddine Berrahou & Salim Bouzebda & Lahcen Douge, 2024. "The Bahadur Representation for Empirical and Smooth Quantile Estimators Under Association," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-37, June.
    9. Fahimah A. Al-Awadhi & Zoulikha Kaid & Ali Laksaci & Idir Ouassou & Mustapha Rachdi, 2019. "Functional data analysis: local linear estimation of the $$L_1$$ L 1 -conditional quantiles," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 217-240, June.
    10. Dehan Kong & Kaijie Xue & Fang Yao & Hao H. Zhang, 2016. "Partially functional linear regression in high dimensions," Biometrika, Biometrika Trust, vol. 103(1), pages 147-159.
    11. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    12. Brooks, C. & Clare, A.D. & Dalle Molle, J.W. & Persand, G., 2005. "A comparison of extreme value theory approaches for determining value at risk," Journal of Empirical Finance, Elsevier, vol. 12(2), pages 339-352, March.
    13. Ping Yu & Zhongzhan Zhang & Jiang Du, 2016. "A test of linearity in partial functional linear regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 953-969, November.
    14. Rice, Gregory & Wirjanto, Tony & Zhao, Yuqian, 2020. "Forecasting value at risk with intra-day return curves," International Journal of Forecasting, Elsevier, vol. 36(3), pages 1023-1038.
    15. Larbi Ait-Hennani & Zoulikha Kaid & Ali Laksaci & Mustapha Rachdi, 2022. "Nonparametric Estimation of the Expected Shortfall Regression for Quasi-Associated Functional Data," Mathematics, MDPI, vol. 10(23), pages 1-23, November.
    16. Yuan, Ming, 2006. "GACV for quantile smoothing splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 813-829, February.
    17. Fatiha Messaci & Nahima Nemouchi & Idir Ouassou & Mustapha Rachdi, 2015. "Local polynomial modelling of the conditional quantile for functional data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(4), pages 597-622, November.
    18. Ufuk Beyaztas & Han Lin Shang & Semanur Saricam, 2025. "Penalized function-on-function linear quantile regression," Computational Statistics, Springer, vol. 40(1), pages 301-329, January.
    19. Huang, Jen-Jsung & Lee, Kuo-Jung & Liang, Hueimei & Lin, Wei-Fu, 2009. "Estimating value at risk of portfolio by conditional copula-GARCH method," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 315-324, December.
    20. Marius Lux & Wolfgang Karl Hardle & Stefan Lessmann, 2020. "Data driven value-at-risk forecasting using a SVR-GARCH-KDE hybrid," Papers 2009.06910, arXiv.org.
    21. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    22. Muge Mutis & Ufuk Beyaztas & Filiz Karaman & Han Lin Shang, 2025. "On function-on-function linear quantile regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 52(4), pages 814-840, March.
    23. Hörmann, Siegfried & Horváth, Lajos & Reeder, Ron, 2013. "A Functional Version Of The Arch Model," Econometric Theory, Cambridge University Press, vol. 29(2), pages 267-288, April.
    24. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    2. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," LIDAM Discussion Papers CORE 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
      • Bauwens, L. & Hafner C. & Laurent, S., 2011. "Volatility Models," LIDAM Discussion Papers ISBA 2011044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
      • Bauwens, L. & Hafner, C. & Laurent, S., 2012. "Volatility Models," LIDAM Reprints ISBA 2012028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Leonidas Tsiaras, 2010. "Dynamic Models of Exchange Rate Dependence Using Option Prices and Historical Returns," CREATES Research Papers 2010-35, Department of Economics and Business Economics, Aarhus University.
    4. Antonio Díaz & Carlos Esparcia, 2021. "Dynamic optimal portfolio choice under time-varying risk aversion," International Economics, CEPII research center, issue 166, pages 1-22.
    5. Drew Creal & Siem Jan Koopman & André Lucas, 2008. "A General Framework for Observation Driven Time-Varying Parameter Models," Tinbergen Institute Discussion Papers 08-108/4, Tinbergen Institute.
    6. Sio Chong U & Jacky So & Deng Ding & Lihong Liu, 2016. "An efficient Fourier expansion method for the calculation of value-at-risk: Contributions of extra-ordinary risks," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 1-27, March.
    7. Rice, Gregory & Wirjanto, Tony & Zhao, Yuqian, 2020. "Forecasting value at risk with intra-day return curves," International Journal of Forecasting, Elsevier, vol. 36(3), pages 1023-1038.
    8. Buccheri, Giuseppe & Corsi, Fulvio & Flandoli, Franco & Livieri, Giulia, 2021. "The continuous-time limit of score-driven volatility models," Journal of Econometrics, Elsevier, vol. 221(2), pages 655-675.
    9. Noori, Mohammad & Hitaj, Asmerilda, 2023. "Dissecting hedge funds' strategies," International Review of Financial Analysis, Elsevier, vol. 85(C).
    10. Ñíguez, Trino-Manuel & Perote, Javier, 2017. "Moments expansion densities for quantifying financial risk," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 53-69.
    11. Marcin Fałdziński & Piotr Fiszeder & Witold Orzeszko, 2020. "Forecasting Volatility of Energy Commodities: Comparison of GARCH Models with Support Vector Regression," Energies, MDPI, vol. 14(1), pages 1-18, December.
    12. Buczyński Mateusz & Chlebus Marcin, 2018. "Comparison of Semi-Parametric and Benchmark Value-At-Risk Models in Several Time Periods with Different Volatility Levels," Financial Internet Quarterly (formerly e-Finanse), Sciendo, vol. 14(2), pages 67-82, June.
    13. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107034723, September.
    14. Weronika Ormaniec & Marcin Pitera & Sajad Safarveisi & Thorsten Schmidt, 2022. "Estimating value at risk: LSTM vs. GARCH," Papers 2207.10539, arXiv.org.
    15. Turan Bali & Panayiotis Theodossiou, 2007. "A conditional-SGT-VaR approach with alternative GARCH models," Annals of Operations Research, Springer, vol. 151(1), pages 241-267, April.
    16. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521547871, September.
    17. Peter Christoffersen & Sílvia Gonçalves, . "Estimation risk in financial risk management," Journal of Risk, Journal of Risk.
    18. Chang, Chia-Lin & González-Serrano, Lydia & Jimenez-Martin, Juan-Angel, 2013. "Currency hedging strategies using dynamic multivariate GARCH," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 164-182.
    19. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    20. Rita Pimentel & Morten Risstad & Sjur Westgaard, 2022. "Predicting interest rate distributions using PCA & quantile regression," Digital Finance, Springer, vol. 4(4), pages 291-311, December.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:13:y:2025:i:12:p:1961-:d:1678875. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.