Bond pricing and yield curve derivation in an extended Keynesian term structure model

This article extends the multifactor Keynesian term structure model proposed by Akram (2023), which postulates that long-term interest rates are influenced by short-term rates and inflation expectations. Building on the theoretical foundation established by the original model for long-term rate dynamics, this article introduces a state-dependent affine structure that enables the derivation of closed-form solutions for bond prices. The long-term rate Rt is modelled as a combination of the short rate rt and the inflation expectation πtE processes, with its volatility depending on its own state, which ensures mathematical tractability and preserves the affine class of the model. Furthermore, a time-decaying weighting function α(t) defines the instantaneous pricing rate x(t,T)=α(t)rt+(1−α(t))Rt, reflecting the declining influence of short-term rates as the maturity horizon increases. The model is further enhanced with jump components in both πtE and Rt, allowing for discontinuities in macro-financial variables. This formulation leads to a system of Riccati equations, solved numerically to obtain bond prices. An empirical calibration to U.S. nominal and real yield curves demonstrates that the jump-augmented model significantly improves fit relative to the original version.