Interest rate options in one-factor mixed modified fractional Vasicek model

Abstract

This paper introduces an innovative interest rate model in which the dynamics of each factor influencing the underlying short-term interest rate is described using a mixed modified fractional Vasicek framework. The study focuses on (a) formulating the short-term interest rate model and identifying its key parameters, including expectations, variance, and the variance–covariance matrix of the model factors, and (b) computing the integral of this novel model to derive zero-coupon bond prices and corresponding yield expressions across maturities, enabling the construction of a robust term structure model based on mixed modified fractional motion. The model is applied to yield curve data from selected Central African countries, including Cameroon, Congo, and Gabon. This involves (i) presenting the observed yield curve data, (ii) estimating model parameters to align with the theoretical framework, and (iii) reconstructing the latent states (underlying factors) of the interest rate model using the Kalman filter algorithm. The comparative analysis between the latent states simulated by the Kalman filter and the theoretical model highlights the algorithm’s efficiency in parameter optimization. Furthermore, the empirical validation in two stages substantiates the robustness and applicability of the model to capture the interest rate dynamics of Central African economies. Beyond its regional focus, this novel framework demonstrates versatility, offering potential applications in modeling interest rate behavior across other emerging and OECD economies.