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Mathematics
Volume 13
Issue 12
10.3390/math13121961
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

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

by
Zouaoui Chikr Elmezouar
1,
Ali Laksaci
1,
Ibrahim M. Almanjahie
1,* and
Fatimah Alshahrani
2
1
Department of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi Arabia
2
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(12), 1961; https://doi.org/10.3390/math13121961 (registering DOI)
Submission received: 10 May 2025 / Revised: 2 June 2025 / Accepted: 7 June 2025 / Published: 13 June 2025
Versions Notes

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.
Keywords: Asymmetric least squares; value at risk; coherent risk measures; expected shortfall; expectile regression; prediction markets; decision making; big-data analysis Asymmetric least squares; value at risk; coherent risk measures; expected shortfall; expectile regression; prediction markets; decision making; big-data analysis

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MDPI and ACS Style

Elmezouar, Z.C.; Laksaci, A.; Almanjahie, I.M.; Alshahrani, F. Nonparametric Estimation of Dynamic Value-at-Risk: Multifunctional GARCH Model Case. Mathematics 2025, 13, 1961. https://doi.org/10.3390/math13121961

AMA Style

Elmezouar ZC, Laksaci A, Almanjahie IM, Alshahrani F. Nonparametric Estimation of Dynamic Value-at-Risk: Multifunctional GARCH Model Case. Mathematics. 2025; 13(12):1961. https://doi.org/10.3390/math13121961

Chicago/Turabian Style

Elmezouar, Zouaoui Chikr, Ali Laksaci, Ibrahim M. Almanjahie, and Fatimah Alshahrani. 2025. "Nonparametric Estimation of Dynamic Value-at-Risk: Multifunctional GARCH Model Case" Mathematics 13, no. 12: 1961. https://doi.org/10.3390/math13121961

APA Style

Elmezouar, Z. C., Laksaci, A., Almanjahie, I. M., & Alshahrani, F. (2025). Nonparametric Estimation of Dynamic Value-at-Risk: Multifunctional GARCH Model Case. Mathematics, 13(12), 1961. https://doi.org/10.3390/math13121961

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