Cash as a Perpetual Option

22 Pages Posted: 22 Sep 2020

Date Written: August 7, 2020


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

Suggested Citation

Andreasen, Jesper and Brøgger, Søren Bundgaard, Cash as a Perpetual Option (August 7, 2020). Available at SSRN: or

Jesper Andreasen

Verition Group LLC ( email )

20 st james street
London, SW1A 1ES
United Kingdom

Søren Bundgaard Brøgger (Contact Author)

Copenhagen Business School ( email )

Solbjerg Plads 3
Frederiksberg C, DK - 2000

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