Social Discounting and the Long Rate of Interest

TL;DR

This paper challenges traditional views on long-term interest rates by introducing models where the long simple rate can fluctuate, enabling better valuation of long-term social projects like climate initiatives.

Contribution

It develops new interest rate models under social discounting assumptions, allowing the long simple rate to serve as a viable state variable with realistic asymptotic behavior.

Findings

Long simple interest rate can fluctuate and serve as a state variable.

Constructed models exhibit good asymptotic properties for discount bonds.

Provides a framework for valuing long-term social projects.

Abstract

The well-known theorem of Dybvig, Ingersoll and Ross shows that the long zero-coupon rate can never fall. This result, which, although undoubtedly correct, has been regarded by many as surprising, stems from the implicit assumption that the long-term discount function has an exponential tail. We revisit the problem in the setting of modern interest rate theory, and show that if the long "simple" interest rate (or Libor rate) is finite, then this rate (unlike the zero-coupon rate) acts viably as a state variable, the value of which can fluctuate randomly in line with other economic indicators. New interest rate models are constructed, under this hypothesis and certain generalizations thereof, that illustrate explicitly the good asymptotic behaviour of the resulting discount bond systems. The conditions necessary for the existence of such "hyperbolic" and "generalized hyperbolic" long rates are those of so-called social discounting, which allow for long-term cash flows to be treated as broadly "just as important" as those of the short or medium term. As a consequence, we are able to provide a consistent arbitrage-free valuation framework for the cost-benefit analysis and risk management of long-term social projects, such as those associated with sustainable energy, resource conservation, and climate change.