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 (arXiv:2010.05462 [q-fin.MF], 2020), which describes joint evolution inflation, central bank interest rate, and short-term rate. In case when diffusion coefficient does not depend on we derive a semi-closed valuation formula for contingent derivatives, in particular Zero Coupon Bonds (ZCBs). By using ZCB yields as observations, implement Kalman filter obtain dynamical estimate turn, by this estimate, at each time step, calibrate parameters under risk-neutral measure risk premium. compare market values German rate several maturities with corresponding predicted our model, from 2007 to 2015. The numerical results validate both procedure.