Modeling bitcoin price by using Euler-Maruyama method

Abstract

<p>In this study, we use Euler-Maruyama method to simulate Bitcoin prices dynamics. We investigate a year-long movement of Bitcoin prices. Daily closing prices were collected over a period starting from May 27th, 2023 and ending on May 27th, 2024. This data provides a comprehensive picture of how Bitcoin behaved on a daily basis throughout that specific year. The Euler-Maruyama method is used as numerical method for solving stochastic differential equations (SDEs). The method involves discretizing the SDE into an iterative process to obtain a simulated price trajectory. The drift term was estimated by the average daily return of Bitcoin prices over the study period. The volatility term was estimated by the standard deviation of daily Bitcoin returns. A Monte Carlo simulation was performed to generate a range of possible price trajectories using the Euler-Maruyama method. The result shows that the Euler-Maruyama method was able to capture the short-term trend of Bitcoin prices effectively. However, the method can also be used to capture the long-term trend of Bitcoin prices.</p>