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All Journal Journal of Information Systems Engineering and Business Intelligence BAREKENG: Jurnal Ilmu Matematika dan Terapan Engineering, Mathematics and Computer Science Journal (EMACS)
Pasaribu, Asysta Amalia
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Civil Engineering, Building, Construction & Architecture Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Industrial & Manufacturing Engineering Mathematics Mechanical Engineering Physics Transportation

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Journal : BAREKENG: Jurnal Ilmu Matematika dan Terapan

 1 
MODEL APPROACH OF AGGREGATE RETURN VOLATILITY: GARCH(1,1)-COPULA VS GARCH(1,1)-BIVARIATE NORMAL Pasaribu, Asysta Amalia; Kurnia, Anang
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp2069-2082

Abstract

Aggregate risk is an aggregation of single risks that are both independent and interdependent. In this study, aggregate risk is constructed from two interdependent random risk variables. The dependence between two random variables can be determined through the size of dependence and joint distribution properties. However, not all distributions have joint distribution properties; the joint distributions may be unknown, so motivating the use of the Copulas in this study is needed. Sometimes, the Copula model is introduced to construct joint distribution properties. The Copula model in this research is used in financial policies such as investment. In the investment sector, the aggregate risk comes from the sum of the single risks and returns. The model used in aggregate return is the Generalized Autoregressive Conditionally Heteroscedastic (GARCH) model. The data used in this study is the closing price data for Apple and Microsoft stocks from January 01, 2010, to January 01, 2024. The best model selection is the model with the GARCH-Bivariate Normal approach with the smallest MSE value. Model GARCH(1,1)-Bivariate Normal is the best model for the volatility model of aggregate return.
COMPARISON OF THE VOLATILITY OF GARCH FAMILY MODEL IN THE CRYPTOCURRENCY MARKET: SYMMETRY VERSUS ASYMMETRY Pasaribu, Asysta Amalia; Sa'adah, Aminatus
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2571-2582

Abstract

Cryptocurrencies can be considered an individual asset class due to their distinct risk/return characteristics and low correlation with other asset classes. Volatility is an important measure in financial markets, risk management, and making investment decisions. Different volatility models are beneficial tools to use for various volatility models. The purpose of this study is to compare the accuracy of various volatility models, including GARCH, EGARCH, and GJR-GARCH. This study applies these volatility models to the Bitcoin, Ethereum, and Litecoin return data in the period January 1st, 2020, to December 31st, 2024. The performance of these models is based on the smallest AIC value for each model. The results of the study indicate that the GARCH (1,1) is the most suitable model for Bitcoin, Litecoin, and Ethereum returns.
Co-Authors Anang Kurnia Aryusmar, Aryusmar I Gusti Agung Anom Yudistira Sa'adah, Aminatus Sasmito, Ayomi