Short-Term Interest Rate Estimation by Filtering in a Model Linking Inflation, the Central Bank and Short-Term Interest Rates

We consider the model of Antonacci, Costantini, D’Ippoliti, Papi (International Journal of Theoretical and Applied Finance, 2021), which describes the joint evolution of inflation, the central bank interest rate, and the short-term interest rate. In the case when the diffusion coefficient does not depend on the central bank interest rate, we derive a semi-closed valuation formula for contingent derivatives, in particular for Zero Coupon Bonds (ZCBs). By using ZCB yields as observations, we implement the Kalman filter and obtain a dynamical estimate of the short-term interest rate. In turn, by this estimate, at each time step, we calibrate the model parameters under the risk-neutral measure and the coefficient of the risk premium. We compare the market values of German interest rate yields for several maturities with the corresponding values predicted by our model, from 2007 to 2015. The numerical results validate both our model and our numerical procedure.