Akademik Veri Yönetim Sistemi
CMES-2025 9th International Conference on Computational Mathematics and Engineering Sciences, Diyarbakır, Türkiye, 17 - 19 Mayıs 2025, ss.10, (Özet Bildiri)
This study examines the USD/TRY exchange rate over the period from April 30, 2015, to April 30, 2025, through a regime-based stochastic differential equation (SDE) modeling framework. Using change point estimation, we identify two structural breaks on November 10, 2021, and March 23, 2022, partitioning the data into three distinct regimes. For each regime, we apply tailored SDEs reflecting their unique statistical characteristics. In Regime 1 (pre-November 2021), a Cox-Ingersoll-Ross (CIR) process is adopted due to its suitability for modeling mean-reverting and strictly positive series with heteroskedasticity. Regime 2 spans a short and turbulent period with limited data, requiring the use of 4-hour interval GBM simulations to enhance sample density for valid calibration. This enriched data enables the application of the Heston stochastic volatility model. In Regime 3 (post-March 2022), characterized by moderately declining volatility, the Heston model continues to provide a flexible structure. The CIR model and Heston models are calibrated using Maximum Likelihood Estimation (MLE), which enables direct parameter inference under each regime’s stochastic structure. By integrating regime-dependent dynamics and simulation-assisted calibration in short regimes, the approach achieves higher fidelity in capturing the evolving behavior of the exchange rate. Overall, the methodology emphasizes the significance of data- driven regime segmentation and stochastic modeling for financial time series in emerging markets.