A New CKLS Model with GARCH-type Volatility and SSAEPD Error Terms

Abstract

This paper introduces a novel extension to the Chan, Karolyi, Longstaff, and Sanders (CKLS) model by incorporating GARCH-type volatility and replacing traditional error terms with Standardized Standard Asymmetric Exponential Power Distribution (SSAEPD) error terms. The classic CKLS model, while robust, fails to account for certain empirical irregularities in financial data such as skewness and fat tails. Our proposed CKLS-GARCH_SSAEPD model aims to address these limitations by integrating the GARCH mechanism for modeling time-varying volatility, as pioneered by Bollerslev (1986), and adopting SSAEPD for error distribution to capture the asymmetry and leptokurtosis in financial datasets. We reevaluate the robustness of the CKLS model using two distinct samples of one-month US Treasury bill yields spanning from 1964 to 2013. The empirical analysis is conducted using Maximum Likelihood Estimation (MLE), with model comparisons based on the Akaike Information Criterion (AIC). Supplementary statistical tests, including the Ljung-Box, Kolmogorov-Smirnov, and Likelihood Ratio tests, are applied to assess the model's fit and robustness. Our findings suggest that the CKLS-GARCH_SSAEPD model provides a better fit to the data compared to the traditional CKLS model, reflecting enhanced capability in capturing the dynamics of interest rate movements and volatility. The modifications introduced in this model significantly improve the understanding and forecasting of interest rates, thereby offering valuable insights for risk management and financial econometrics.