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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan Bulletin of Applied Mathematics and Mathematics Education
Staenly, Staenly
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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Simulating Bitcoin price movements with the Bates model and Monte Carlo methods Staenly, Staenly; Irsan, Maria Yus Trinity
Bulletin of Applied Mathematics and Mathematics Education Vol. 5 No. 1 (2025)
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12928/bamme.v5i1.12815

Abstract

This study investigates the price dynamics of Bitcoin, a highly volatile and speculative digital asset. Using daily closing price data from January 2023 to January 2024, we apply the Bates model, which combines stochastic volatility with jump-diffusion processes, to better capture both continuous fluctuations and sudden, large price changes in the market. The model parameters are calibrated using historical data and evaluated through Monte Carlo simulation with 10,000 generated price paths over a 31-day forecast horizon. The results demonstrate a strong short-term predictive performance, with a Mean Absolute Percentage Error (MAPE) of 4.32%. This indicates that the Bates model can capture both volatility clustering and abrupt shifts, which are characteristic of Bitcoin. The findings suggest that this approach provides a valuable tool for risk management and investment decision-making in highly uncertain and dynamic markets.
OPTIMAL CRYPTOCURRENCY PORTFOLIO CONSTRUCTION USING GARCH-BASED MONTE CARLO SIMULATION Staenly, Staenly; Irsan, Maria Yus Trinity; Ginting, Josep
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1035-1046

Abstract

This study investigates the construction of an optimal cryptocurrency portfolio comprising Ethereum and Solana using a GARCH-based Monte Carlo simulation framework. Asset volatilities were modelled individually through GARCH (1,1) processes, while asset correlations were captured using standardized residuals and Cholesky decomposition. Simulation results over 180- and 360-day horizons showed that the optimized portfolio achieved slightly higher cumulative growth factors and better upside capture compared to an equal-weighted benchmark, particularly during volatile market phases. In out-of-sample testing, the return-to-risk optimized portfolio delivered a total return of 34% over six months, compared to 33% for the equal-weighted strategy, while maintaining a higher return-to-risk ratio (0.06 versus 0.05) and lower volatility (3% versus 4%). Over a one-year period, both portfolios converged closely, with the equal-weighted strategy achieving a slightly higher total return of 45% compared to 43% for the optimized portfolio. These findings suggest that GARCH-based optimization can enhance portfolio resilience and risk-adjusted returns, although its realized return advantage may diminish in synchronized market conditions.
Co-Authors Irsan, Maria Yus Trinity Josep Ginting