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

Sevda Ozdemır Calikusu; Fevzi Erdoğan; Nihal İnce

doi:10.33187/jmsm.1643023

EN

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

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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Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Sevda Ozdemır Calikusu ^*
0000-0002-0238-2677
Türkiye

Fevzi Erdoğan
0000-0003-3745-0198
Türkiye

Nihal İnce
0000-0001-6684-5848
Türkiye

Early Pub Date

June 18, 2025

Publication Date

June 28, 2025

Submission Date

February 19, 2025

Acceptance Date

June 13, 2025

Published in Issue

Year 2025 Volume: 8 Number: 2

DOI

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

IZ

https://izlik.org/JA36RX79HD

APA

Ozdemır Calikusu, S., Erdoğan, F., & İnce, N. (2025). 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. Journal of Mathematical Sciences and Modelling, 8(2), 75-85. https://doi.org/10.33187/jmsm.1643023

AMA

1.Ozdemır Calikusu S, Erdoğan F, İnce N. 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. Journal of Mathematical Sciences and Modelling. 2025;8(2):75-85. doi:10.33187/jmsm.1643023

Chicago

Ozdemır Calikusu, Sevda, Fevzi Erdoğan, and Nihal İnce. 2025. “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”. Journal of Mathematical Sciences and Modelling 8 (2): 75-85. https://doi.org/10.33187/jmsm.1643023.

EndNote

Ozdemır Calikusu S, Erdoğan F, İnce N (June 1, 2025) 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. Journal of Mathematical Sciences and Modelling 8 2 75–85.

IEEE

[1]S. Ozdemır Calikusu, F. Erdoğan, and N. İnce, “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”, Journal of Mathematical Sciences and Modelling, vol. 8, no. 2, pp. 75–85, June 2025, doi: 10.33187/jmsm.1643023.

ISNAD

Ozdemır Calikusu, Sevda - Erdoğan, Fevzi - İnce, Nihal. “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”. Journal of Mathematical Sciences and Modelling 8/2 (June 1, 2025): 75-85. https://doi.org/10.33187/jmsm.1643023.

JAMA

1.Ozdemır Calikusu S, Erdoğan F, İnce N. 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. Journal of Mathematical Sciences and Modelling. 2025;8:75–85.

MLA

Ozdemır Calikusu, Sevda, et al. “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”. Journal of Mathematical Sciences and Modelling, vol. 8, no. 2, June 2025, pp. 75-85, doi:10.33187/jmsm.1643023.

Vancouver

1.Sevda Ozdemır Calikusu, Fevzi Erdoğan, Nihal İnce. 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. Journal of Mathematical Sciences and Modelling. 2025 Jun. 1;8(2):75-8. doi:10.33187/jmsm.1643023