CONSISTENCY CONDITIONS FOR AFFINE TERM STRUCTURE MODELS

Abstract. ATSM are widely applied for pricing of bonds and in-terest rate derivatives but the consistency of ATSM when the short rate, r, is unbounded from below remains essentially an open ques-tion. First, the standard approach to ATSM uses the Feynman-Kac theorem which is easily applicable only when r is bounded from below. Second, if the tuple of state variables belongs to the region where r is positive, the bond price should decrease in any state variable for which the corresponding coefficient in the formula for r is positive; the bond price should also decrease as the time to maturity increases. In the paper, sufficient conditions for the ap-plication of the Feynman-Kac formula, and monotonicity of the bond price are derived, for wide classes of affine term structure models in the pure diffusion case. Necessary conditions for the monotonicity are obtained as well. The results can be generalized for jump-diffusion processes. Key words affine term structure models, Feynman-Kac formula The author is grateful to Darrel Duffie for the indication that the use of the Feyman-Kac theorem in ATSM is not justified even for many diffusion processes, and illuminating discussions. The author is thankful to the participants of a semina