Positive Interest Rates and Yields: Additional Serious Considerations*

Over the past quarter century, mathematical modeling of the behavior of the interest rate and the resulting yield curve has been a topic of considerable interest. In the continuous-time modeling of stock prices, one only need specify the diffusion term, because the assumption of risk-neutrality for pricing identifies the expected change. But this is not true for yield curve modeling. This paper explores what types of diffusion and drift terms forbid negative yields, but nevertheless allow any yield to be arbitrarily close to zero. We show that several models have these characteristics; however, they may also have other odd properties. In particular, the square root model of Cox–Ingersoll–Ross has such a solution, but only in a singular case. In other cases, bubbles will occur in bond prices leading to unusually behaved solutions. Other models, such as the CIR three-halves power model, are free of such oddities.