Cash as a Perpetual Option

Abstract

We consider the option value of cash when nominal interest rates are no longer constrained by the zero lower bound. We provide a general valuation principle and solve for the value of cash in semi-closed form under Vasicek (1977) dynamics for the nominal short rate. In the absence of a zero lower bound, cash can have substantial option value and becomes a powerful recessionary hedge. However, a significant fraction of the value derives from the ability to hold cash over an extremely long horizon, and the risk of early redemption decreases the value and hedging performance of cash.

Keywords: cash, nominal interest rates, zero lower bound, monetary policy, perpetual claims

JEL Classification: G12, G13, E50, E58