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All Journal Jambura Journal of Mathematics MEJ (Mathematics Education Journal) KUBIK: Jurnal Publikasi Ilmiah Matematika JURNAL LENTERA AKUNTANSI Assets : Jurnal Ilmiah Ilmu Akuntansi, Keuangan dan Pajak Polinomial : Jurnal Pendidikan Matematika Economics, Business, Management, & Accounting Journal Jurnal Pengabdian Masyarakat Journal of Mathematics, Computation and Statistics (JMATHCOS)
Paiz Jalaludin
Universitas Darunnajah
Religion Agriculture, Biological Sciences & Forestry Humanities Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Mathematics Physics Social Sciences

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Journal : Journal of Mathematics, Computation and Statistics (JMATHCOS)

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Backtesting of the Value-at-Risk Based on GARCH Model (VaR-GARCH) in Measuring Stock Market Risk Mufaridho, Lailatul Maziyah Wildan; SH, Khaerun Nisa; Jalaludin, Paiz; Pratama, Muhammad Isbar
Journal of Mathematics, Computations and Statistics Vol. 9 No. 1 (2026): Volume 09 Issue 01 (March 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/eyqd4722

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.
Co-Authors Alrafiful Rahman Amigo, Royyan Andirasdini, Indah Gumala Ani Nuraini Ani Nuraini Dewi Susanawati Hamdi At-Taibi, Faisal Jahrani, Siti Krishna Prafidya Romantica Lailatul Maziyah Wildan Mufaridho Muhammad Isbar Pratama Rahman, Alrafiful Romantica , Krishna Prafidya Romantica, Krishna Prafidya Royyan Amigo SH, Khaerun Nisa Susanawati, Dewi