A Short‐Rate Model With Stochastic Long‐Term Mean and Volterra‐Type Memory: Risk Implications for Bonds and Option Pricing

ABSTRACT Traditional short‐rate models introduce volatility directly into the instantaneous rate via Brownian shocks. However, empirical data suggest that short‐term interest rates exhibit smoother behavior than such models imply. We propose a two‐factor Gaussian short‐rate model in which the short rate is a deterministic exponential filter of a stochastic mean‐reverting latent mean. The randomness enters exclusively through a latent Ornstein‐Uhlenbeck process representing long‐term expectations, yielding a two‐dimensional affine Markov structure in the state variables, while the short rate itself admits a non‐Markovian Volterra‐type representation. A closed‐form exponential‐affine characteristic function for the integrated rate is derived, allowing for analytical bond pricing and Fourier‐based derivative valuation. Empirical results on U.S. Treasury data show that the model outperforms the Vasicek benchmark in both in‐sample fit and out‐of‐sample forecasting, with a reduction in RMSE. The model yields stable and economically interpretable parameters while requiring only a single source of randomness. Its mathematical tractability offers a compelling alternative for interest rate modeling, monetary policy analysis, and risk management.