Taking Positive Interest Rates Seriously

We propose a dynamic term structure model where interest rates of all maturities are bounded from below at zero. We show that positivity and continuity, combined with no arbitrage, impose such a tight restriction on the term structure that only one functional form is possible. Even more strikingly, the term structure is governed by exactly three sources of risk, only one of which is dynamic. This one dynamic source controls the level of the interest rate and follows a special twoparameter square root process under the risk-neutral measure. The two parameters of the process determine the other two sources of risk and can be regarded as two static factors. Thus, unlike traditional models, this has no other parameters to estimate and hence no other risks to bear. We cast the model into a state space framework and estimate the model on both U.S. Treasury yields and U.S. dollar swap rates. Despite its extreme simplicity, the model fits the term structures of both markets well. The pricing errors are mostly within a few basis points. JEL Classification Codes: E43, G12, G13.