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

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 tha...

Full description

Saved in:
Bibliographic Details
Main Authors: Nihal İnce, Fevzi Erdoğan, Sevda Ozdemır Calikusu
Format: Article
Language:English
Published: Mahmut Akyigit 2025-06-01
Series:Journal of Mathematical Sciences and Modelling
Subjects:
Online Access:https://dergipark.org.tr/en/download/article-file/4623757
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849428462144585728
author Nihal İnce
Fevzi Erdoğan
Sevda Ozdemır Calikusu
author_facet Nihal İnce
Fevzi Erdoğan
Sevda Ozdemır Calikusu
author_sort Nihal İnce
collection DOAJ
description 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.
format Article
id doaj-art-e53847afe2ab4707b58b1dec833912c8
institution Kabale University
issn 2636-8692
language English
publishDate 2025-06-01
publisher Mahmut Akyigit
record_format Article
series Journal of Mathematical Sciences and Modelling
spelling doaj-art-e53847afe2ab4707b58b1dec833912c82025-08-20T03:28:41ZengMahmut AkyigitJournal of Mathematical Sciences and Modelling2636-86922025-06-0182758510.33187/jmsm.16430231408Geometric Brownian Motion Based on Stochastic Differential Equation Modeling Considering the Change Point Estimation for the Fluctuation of the Turkish Lira Against the US DollarNihal İnce0https://orcid.org/0000-0001-6684-5848Fevzi Erdoğan1https://orcid.org/0000-0003-3745-0198Sevda Ozdemır Calikusu2https://orcid.org/0000-0002-0238-2677ESKISEHIR TECHNICAL UNIVERSİTYVAN YUZUNCU YIL UNIVERSITYYUZUNCU YIL UNIVERSITY, ÖZALP VOCATIONAL SCHOOLIn 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.https://dergipark.org.tr/en/download/article-file/4623757change point estimationeuler-maruyama approximation methodgeometric brownian motionitô stochastic differential equationmaximum likelihood estimation method
spellingShingle Nihal İnce
Fevzi Erdoğan
Sevda Ozdemır Calikusu
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
change point estimation
euler-maruyama approximation method
geometric brownian motion
itô stochastic differential equation
maximum likelihood estimation method
title 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
title_full 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
title_fullStr 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
title_full_unstemmed 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
title_short 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
title_sort 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
topic change point estimation
euler-maruyama approximation method
geometric brownian motion
itô stochastic differential equation
maximum likelihood estimation method
url https://dergipark.org.tr/en/download/article-file/4623757
work_keys_str_mv AT nihalince geometricbrownianmotionbasedonstochasticdifferentialequationmodelingconsideringthechangepointestimationforthefluctuationoftheturkishliraagainsttheusdollar
AT fevzierdogan geometricbrownianmotionbasedonstochasticdifferentialequationmodelingconsideringthechangepointestimationforthefluctuationoftheturkishliraagainsttheusdollar
AT sevdaozdemırcalikusu geometricbrownianmotionbasedonstochasticdifferentialequationmodelingconsideringthechangepointestimationforthefluctuationoftheturkishliraagainsttheusdollar