Journal of Mathematics, Computation and Statistics (JMATHCOS)
Vol. 9 No. 1 (2026): Volume 09 Issue 01 (March 2026)

Backtesting of the Value-at-Risk Based on GARCH Model (VaR-GARCH) in Measuring Stock Market Risk

Lailatul Maziyah Wildan Mufaridho (Sains Aktuaria, Universitas Darunnajah)
Khaerun Nisa SH (Akuntansi, Fakultas Ekonomi dan Bisnis, Universitas Negeri Makassar)
Paiz Jalaludin (Sains Aktuaria, Universitas Darunnajah)
Muhammad Isbar Pratama (Universitas Negeri Makassar)



Article Info

Publish Date
03 Mar 2026

Abstract

Accurate market risk measurement is a crucial aspect of stock portfolio management, particularly in volatile market conditions. One commonly used method for measuring market risk is Value-at-Risk (VaR). However, the conventional VaR approach often fails to capture the dynamics of volatile volatility. Therefore, this study aims to measure stock market risk using a GARCH-based Value-at-Risk approach and test the model's reliability using the Kupiec Proportion of Failures Test. The data used are daily stock price data processed into logarithmic returns. Return volatility is estimated using the GARCH(1,1) model, and the VaR value is calculated based on conditional volatility at a 5 percent significance level. VaR backtesting is then performed to identify violations and evaluate the model's validity using the Kupiec Test. The results of the study show that out of 653 observations, there were 27 VaR violations, with a Kupiec statistic value of 1.0909 and a p-value of 0.2963. A p-value greater than the significance level indicates that the VaR–GARCH model is statistically valid and able to measure market risk well. This study concludes that the VaR–GARCH approach is a reliable method in measuring stock market risk and can be used as a supporting tool in investment decision-making and risk management.

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Journal Info

Abbrev

JMATHCOS

Publisher

Subject

Mathematics

Description

Fokus yang didasarkan tidak hanya untuk penelitian dan juga teori-teori pengetahuan yang tidak menerbitkan plagiarism. Ruang lingkup jurnal ini adalah teori matematika, matematika terapan, program perhitungan, perhitungan matematika, statistik, dan statistik ...