Money as Options

Abstract

The demand for money depends crucially on nominal short rates since investors can, in principle, withdraw from deposit accounts to avoid negative interest rates. Thus, money is an option, which in turn implies the nominal short rate is an option written on a `shadow' rate. We develop this argument in general equilibrium and reveal a novel result. The relationship between the nominal rate and shadow rate has a discontinuity such that the nominal rate jumps to zero before the shadow rate reaches it from above. As observed empirically, this generates a strong deflationary-inflationary reaction at close to zero interest rates. In addition, optionality in money generates a testable prediction for the dynamics of short dated interest rate volatility. Studying this prediction, we show that the interest rate volatility term structure becomes flat and even inverts for short maturity money market rates at the lower bound.

Keywords: Interest rates, inflation, deflation, money, lower bound, general equilibrium.

JEL Classification: E0, E31, E41, E43, G12, G13