Simulating Bitcoin price movements with the Bates model and Monte Carlo methods

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.