A comparative study of cox-ingersoll-ross and Vasicek models: a case study of the 91-day treasury Bill rate in Kenya

Abstract

Interest rates is an important factor in the operation of any financial market, with different interest rates having different effects on investment decisions. As such, understanding how interest rates move across different markets can be a crucial factor in managing market risk and maximizing returns. The success of financial investments heavily relies on accurately predicting changes in the rates of interest. The objective of the research was to compare between the Vasicek andCIR model, more accurately captures dynamics of interest rates in Kenya. The reason for choosing these models is they are commonly used because they are analytically tractable and easy to implement. To achieve the objective of this study, we estimated parameters for the models.We compared the performance of both models in predicting future interest rate values. Data on the Treasury bill rates with 91 days maturities was used from the website of the CBK as a proxy of interest rate from July 2019 to September 2023. Parameters were derived using the Ordinary Least Squares technique. An advantage of using the method is that it is easy to implement and handles large data sets efficiently. Microsoft Excel was employed for data simulation. The estimates obtained from both the CIR and Vasicek Models were then used to determine which one better fit the available data, with the research recommending the use of the Vasicek Model due to its stable simulated data and the absence of any significant difference between its test statistics and the actual data. However, caution should be exercised when applying both the Vasicek and CIR models. These findings can serve as a foundation for developing more effective predictive tools for forecasting future interest rate values in Kenya, enhancing the accuracy and robustness of financial analysis and research in this domain.