Backtesting of the Value-at-Risk Based on GARCH Model (VaR-GARCH) in Measuring Stock Market Risk - Lailatul Maziyah Wildan Mufaridho; Khaerun Nisa SH; Paiz Jalaludin; Muhammad Isbar Pratama (Journal of Mathematics, Computations and Statistics, 2026)
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.