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Boundary conditions for the single-factor term structure equation
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2011 (English)In: The Annals of Applied Probability, ISSN 1050-5164, E-ISSN 2168-8737, Vol. 21, no 1, 332-350 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2011. Vol. 21, no 1, 332-350 p.
Keyword [en]
The term structure equation, degenerate parabolic equations, stochastic representation
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-119598DOI: 10.1214/10-AAP698ISI: 000286359600011OAI: oai:DiVA.org:uu-119598DiVA: diva2:300534
Available from: 2010-02-26 Created: 2010-02-26 Last updated: 2017-12-12

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Ekström, Erik

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