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

Zouaoui Chikr-Elmezouar, Ali Laksaci, Ibrahim M. Almanjahie () and Fatimah Alshahrani
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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

Mathematics, 2025, vol. 13, issue 12, 1-20

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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