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All Journal M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika International Journal of Quantitative Research and Modeling
Kalfin Kalfin
Universitas Negeri Makassar
Computer Science & IT Decision Sciences, Operations Research & Management Education Engineering Environmental Science Mathematics Physics

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Analysis of Stock Return Volatility of PT Asuransi Multi Artha Guna Tbk Using the GARCH-M Model Muh. Yahya; Kalfin Kalfin; Hisyam Ihsan; Atikafairuq Selviana; Andi Widya Pratiwi Anas
International Journal of Quantitative Research and Modeling Vol. 7 No. 2 (2026): International Journal of Quantitative Research and Modeling (IJQRM)
Publisher : Research Collaboration Community (RCC)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46336/ijqrm.v7i2.1334

Abstract

This study aims to analyze the volatility of stock returns of PT Asuransi Multi Artha Guna Tbk using the Generalized Autoregressive Conditional Heteroskedasticity in Mean (GARCH-M) model during the 2019–2024 period. The data used in this study are secondary data in the form of daily closing stock prices of AMAG.JK obtained from Yahoo Finance, with a total of 1,466 observations. The analytical stages include the calculation of log returns, stationarity testing using the Augmented Dickey-Fuller (ADF) test, Ljung-Box autocorrelation test, ARCH-LM test, selection of the best GARCH model based on the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), estimation of the GARCH-M model, conditional volatility analysis, and volatility forecasting. The results indicate that the stock return data of AMAG.JK are stationary and contain ARCH effects, making them appropriate for analysis using the GARCH model. Based on the AIC and BIC criteria, the best model selected is GARCH(1,2). The estimation results of the GARCH(1,2)-M model show that the ARCH and GARCH parameters are statistically significant, indicating the presence of volatility clustering and volatility persistence phenomena in the stock returns of AMAG.JK. However, the risk premium parameter in the GARCH-M model is not statistically significant, implying that conditional volatility does not significantly affect expected stock returns. The volatility forecasting results show that the volatility level of AMAG.JK stock tends to increase gradually in future periods. Overall, the GARCH(1,2)-M model is capable of describing the dynamics of volatility in AMAG.JK stock returns during the research period effectively.
Insurance Premium Determination Model Using The Cobb-Douglas Regression Method On Shallot Production Jeremi Heryandi Saudi; Kalfin Kalfin; Ni Luh Sri Diantini
Mathline : Jurnal Matematika dan Pendidikan Matematika Vol. 10 No. 4 (2025): Mathline : Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas Wiralodra

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31943/mathline.v10i4.1051

Abstract

The production risk of shallots is very high due to their vulnerability to pest attacks, diseases, and climate change, which creates uncertainty that may cause significant losses for farmers. Insurance protection has therefore become a necessity as an effort to mitigate financial losses and maintain farmers’ stability even in the event of crop failure. Accordingly, this study aims to analyze the production factors of shallots in determining agricultural insurance premiums. The study employs the Cobb-Douglas production function to analyze production factors and the pure premium model to calculate shallot insurance premiums. Data were collected through questionnaires distributed to shallot farmers in Tasikmalaya Regency, with 50 respondents included in the analysis. Based on the results, the determination of shallot insurance premiums using the expectation principle produces higher premium values compared to the standard deviation principle. Premiums under the expectation principle are more sensitive to risk variation, whereas the standard deviation principle tends to yield more conservative and relatively stable premiums. The analysis applies the Cobb-Douglas regression model, with shallot production (Y) as the dependent variable, and land area (X1), seeds (X2), fertilizer (X3), pesticide use (X4), and labor (X5) as independent variables, resulting in a coefficient of determination (R²) of 96.2%. The findings imply that the expectation principle is more appropriate for calculating insurance premiums under conditions of high and fluctuating production risk, while the standard deviation principle is more suitable for relatively stable risk conditions. These results can serve as a basis for formulating agricultural insurance policies that are adaptive to risk variation, while simultaneously promoting more effective financial protection for shallot farmers.
Co-Authors Andi Widya Pratiwi Anas Atikafairuq Selviana Hisyam Ihsan Jeremi Heryandi Saudi Muh. Yahya Ni Luh Sri Diantini