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  4. Modeling short term interest rates using the Vasicek and Cox–Ingersoll–Ross models

Modeling short term interest rates using the Vasicek and Cox–Ingersoll–Ross models

MMC.
2025;
Volume 12, Number 1
: pp. 212–220
https://doi.org/10.23939/mmc2025.01.212
Received: November 19, 2024
Revised: February 17, 2025
Accepted: February 19, 2025

Md Sa'at A. S., Shair S. N., Md Lazam N., Yusof A. Y., Mohd Amin M. N., Ibrahim R. I., Mohd Ghani N. A.  Modeling short term interest rates using the Vasicek and Cox–Ingersoll–Ross models.  Mathematical Modeling and Computing. Vol. 12, No. 1, pp. 212–220 (2025) 

Authors:
  1. A. S. Md Sa'at
  2. S. N. Shair
  3. N. Md Lazam
  4. A. Y. Yusof
  5. M. N. Mohd Amin
  6. R. I. Ibrahim
  7. N. A. Mohd Ghani
1
School of Mathematical Sciences, College of Computing, Informatics and Mathematics, University Teknologi MARA (UiTM)
2
School of Mathematical Sciences, College of Computing, Informatics and Mathematics, University Teknologi MARA (UiTM); Research Interest Group of Actuarial Risk, Analytics and Takaful, Universiti Teknologi MARA (UiTM)
3
School of Mathematical Sciences, College of Computing, Informatics and Mathematics, University Teknologi MARA (UiTM); Research Interest Group of Actuarial Risk, Analytics and Takaful, Universiti Teknologi MARA (UiTM)
4
School of Mathematical Sciences, College of Computing, Informatics and Mathematics, University Teknologi MARA (UiTM)
5
School of Mathematical Sciences, College of Computing, Informatics and Mathematics, University Teknologi MARA (UiTM); Research Interest Group of Actuarial Risk, Analytics and Takaful, Universiti Teknologi MARA (UiTM)
6
Faculty of Science and Technology, University Sains Islam Malaysia
7
School of Mathematical Sciences, College of Computing, Informatics and Mathematics, University Teknologi MARA (UiTM)

In modeling future uncertainties, the time value of money effect is often minimally addressed.  Many models assume constant rates, leading to potential errors in financial instrument pricing.  This study explores continuous-time interest rate models to capture future uncertainties of interest rates.  Two stochastic interest rate models, the Vasicek and Cox–Ingersoll–Ross (CIR), will be adopted, and their forecast performance will be evaluated.  Using the Maximum Likelihood Estimation (MLE), the models are fitted to Kuala Lumpur Interbank Offered Rate (KLIBOR) data (1-month, 3-month, and 12-month rates).  Subsequently, the goodness-of-fit and forecast accuracies of both models were analysed.  Results show that the Vasicek model is superior based on AIC, BIC, MSE, RMSE, and MAPE measures.  The Vasicek model outperforms CIR, especially for 12-month rates.  Finally, this study estimates zero-coupon bond prices and develops the term structure of interest rates, revealing an inverted yield curve.

stochastic modeling; interest rate risk; Vasicek model; Cox–Ingersoll–Ross model
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