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...
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| Format: | Article |
| Language: | English |
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Mahmut Akyigit
2025-06-01
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| Series: | Journal of Mathematical Sciences and Modelling |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/4623757 |
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| 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 |