Application of GARCH and Value-at-Risk (VaR) Models in Stochastic Analysis of LQ45 Index Volatility

Stock market volatility is a crucial factor in investment decision-making. This study analyzes the volatility of the LQ45 Index, one of Indonesia's major stock indices, using the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model and assesses risk through the Value-at-Risk (VaR) method. The data consists of daily closing prices of the LQ45 index from 2020 to 2024. A GARCH(1,1) model is used to estimate the conditional variance dynamically, and VaR is calculated at the 95% confidence level. The results show that the GARCH(1,1) model effectively captures volatility dynamics, with the highest daily VaR recorded at 3.21% during the first quarter of 2020. The novelty of this study lies in the explicit integration of the mathematical formulation of GARCH with VaR estimation in the context of the Indonesian stock market, particularly the LQ45 index, which is rarely addressed in pure mathematical finance literature. This approach contributes to the development of stochastic financial models and provides a quantitative framework for investment risk management.