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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, 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
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