Geometric Brownian Motion Based on Stochastic Differential Equation Modeling Considering the Change Point Estimation for the Fluctuation of the Turkish Lira Against the US Dollar

Year 2025, Volume: 8 Issue: 2, 75 - 85, 28.06.2025

Sevda Ozdemır Calikusu , Fevzi Erdoğan , Nihal İnce

https://doi.org/10.33187/jmsm.1643023

Abstract

In this study, the data showing the fluctuation of the Turkish Lira (TL) against the US Dollar (USD) between 19.06.2017 and 19.06.2022 were examined with Geometric Brownian Motion Stochastic Differential Equation Modeling (GBM SDEM). The study aims to get the GBM stochastic differential equation that best fits USD/TL data by considering the change point estimation (CP). Considering CP when working with abruptly changing datasets has a positive effect on the performance of the constructed model. In addition, there may be more than one CP in the data set, and as the number of CP increases, more suitable models can be obtained for the dataset. The results are supported by graphs that show the proposed SDE model fits the dataset.

Keywords

Change point estimation, Euler-Maruyama approximation method, Geometric Brownian Motion, Itô stochastic differential equation, Maximum likelihood estimation method

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