Boundary conditions for the single-factor term structure equation

Details Boundary conditions for the single-factor term structure equation Boundary conditions for the single-factor term structure equation

2011-01-06

arxiv.org/abs/1101.1149v1

Annals of Applied Probability 2011, Vol. 21, No. 1, 332-350

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AAP698 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/10-AAP698

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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