Open Access
Translator Disclaimer
May, 1995 Black's Consol Rate Conjecture
Darrell Duffie, Jin Ma, Jiongmin Yong
Ann. Appl. Probab. 5(2): 356-382 (May, 1995). DOI: 10.1214/aoap/1177004768


This paper confirms a version of a conjecture by Fischer Black regarding consol rate models for the term structure of interest rates. A consol rate model is one in which the stochastic behavior of the short rate is influenced by the consol rate. Since the consol rate is itself determined, via the usual discounted present value formula, by the short rate, such models have an inherent fixed point aspect. Under an equivalent martingale measure, purely technical regularity conditions are given for the stochastic differential equation defining the short rate and the consol rate to be consistent with the definition of the consol rate as the yield on a perpetual annuity. The results are based on an extension of the theory for the forward-backward stochastic differential equations to infinite-horizon settings. Under additional compatibility conditions, we also show that the consol rate is uniquely determined and given as a function of the short rate.


Download Citation

Darrell Duffie. Jin Ma. Jiongmin Yong. "Black's Consol Rate Conjecture." Ann. Appl. Probab. 5 (2) 356 - 382, May, 1995.


Published: May, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0830.60052
MathSciNet: MR1336873
Digital Object Identifier: 10.1214/aoap/1177004768

Primary: 60H10
Secondary: 60H20 , 90A12 , 90A16

Keywords: consol rate problem , Forward-backward stochastic differential equations , nodal solutions , Term structure of interest rates

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.5 • No. 2 • May, 1995
Back to Top