Please use this identifier to cite or link to this item: http://buratest.brunel.ac.uk/handle/2438/12100
Title: Social discounting and the long rate of interest
Authors: Brody, DC
Hughston, LP
Keywords: Interest rate models;Dybvig-Ingersoll-Ross theorem;Long rate;Social discounting;Pricing kernel;Hyperbolic discount function;Declining discount rate
Issue Date: 2016
Publisher: Wiley
Citation: Mathematical Finance, Forthcoming, (2016)
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.
URI: http://bura.brunel.ac.uk/handle/2438/12100
Appears in Collections:Dept of Mathematics Research Papers

Files in This Item:
File Description SizeFormat 
Fulltext.pdfFile is embargoed until 01/04/2018166.17 kBAdobe PDFView/Open    Request a copy


Items in BURA are protected by copyright, with all rights reserved, unless otherwise indicated.