BOUNDARY CONDITIONS FOR THE SINGLE-FACTOR TERM STRUCTURE EQUATION

• 成果类型: Article
• 署名作者: Ekstrom, Erik; Tysk, Johan
• 署名单位: Uppsala University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/10-AAP698
• 发表日期: 2011
• 页码: 332-350
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; chains

摘要

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.