Interest Rates as Options

Since people can hold currency at a zero nominal interest rate, the nominal short cannot be negative. The real interest can be and has been negative, since low risk real investment opportunities, like filling in the Mississippi delta, do not guarantee positive returns. The inflation can be and has been negative, most recently (in the U.S.) during the Great Depression. The nominal short is the shadow real interest rate (as defined by the investment opportunity set) plus the inflation rate, or zero, whichever is greater. Thus the nominal short is an option. Longer term interest rates are always positive, since the future short may be positive even when the current short is zero. We can easily build this option element into our interest trees for backward induction or Monte Carlo simulation: just create a distribution that allows negative nominal rates, and then replace each negative with zero.