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February 2011 Boundary conditions for the single-factor term structure equation
Erik Ekström, Johan Tysk
Ann. Appl. Probab. 21(1): 332-350 (February 2011). DOI: 10.1214/10-AAP698

Abstract

We study the term structure equation for single-factor models that predict nonnegative short rates. In particular, we show that the price of a bond or a bond option is the unique classical solution to a parabolic differential equation with a certain boundary behavior for vanishing values of the short rate. If the boundary is attainable then this boundary behavior serves as a boundary condition and guarantees uniqueness of solutions. On the other hand, if the boundary is nonattainable then the boundary behavior is not needed to guarantee uniqueness but it is nevertheless very useful, for instance, from a numerical perspective.

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Erik Ekström. Johan Tysk. "Boundary conditions for the single-factor term structure equation." Ann. Appl. Probab. 21 (1) 332 - 350, February 2011. https://doi.org/10.1214/10-AAP698

Information

Published: February 2011
First available in Project Euclid: 17 December 2010

zbMATH: 1232.91679
MathSciNet: MR2759205
Digital Object Identifier: 10.1214/10-AAP698

Subjects:
Primary: 91B28
Secondary: 35A05, 35K65, 60J60

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.21 • No. 1 • February 2011
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