Initial Value Problem and Solution for Dynamic Term Structure with Predictable Risk-free Interest Rate

The existence of a non-stochastic or predictable risk-free interest rate has been a critical premise in financial economics. In equity and equity option pricing, since default-free bonds are assumed as risk-free assets, the risk-free interest rate may be approximated by the observable yields of short-term Treasury bills. If the dynamics of the entire term structure cannot be ignored, since none of the observable yields is risk-free, the risk-free interest rate must be an unobservable yet predictable common return on all riskless bond portfolios, which should be identifiable by a dynamic term structure model. However, the existing dynamic term structure models have all asserted the risk-free return on riskless bond portfolios as the stochastic instantaneous spot rate. The existence of a predictable risk-free interest rate has never been empirically verified because it has been precluded.