Modeling and Forecasting Excess Market Returns Using a Two-Factor CIR Model

Abstract

Excess market return (Mkt) plays a central role in modern asset pricing models. However, forecasting market excess returns remains challenging due to their nonlinear dynamics, strong volatility, and structural changes, particularly in emerging markets. This study proposes a two factor Cox–Ingersoll–Ross (CIR2) stochastic model to capture the dynamic behavior of excess market returns in Vietnam. The dataset consists of the VN-Index and the one-year Vietnamese government bond yield covering the period from January 2010 to March 2025. To satisfy the positivity condition required by the CIR diffusion process, excess returns are transformed by adding a constant shift. The parameters of the proposed model are estimated using a maximum likelihood approach based on a discretized representation of the stochastic differential equations. To evaluate predictive performance, an out-of-sample forecasting experiment is conducted using a rolling-window framework with a window length of 36 months. The forecasting ability of the CIR2 model is compared with several benchmark models commonly used in financial time-series forecasting, including the Random Walk, ARIMA, and GARCH(1,1) models. The empirical results indicate that the proposed two-factor CIR model consistently achieves lower forecasting errors than the benchmark models. The improvement in predictive performance is further supported by the Diebold–Mariano test. These findings suggest that stochastic diffusion models with mean-reverting dynamics provide a flexible framework for modeling financial return dynamics in emerging markets and offer useful insights for asset pricing, portfolio management, and financial risk monitoring.