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, im...