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Tractable forms of the bond pricing equation. (English) Zbl 1112.91035

Summary: So far, a small number of analytically tractable single-factor models have been devised for the well-known bond pricing equation (BPE). In this paper, new tractable models are formulated in a systematic manner. First, the BPE is transformed to a standard canonical form in which only one coefficient function appears. In some interesting cases, this single coefficient function is identically zero, leaving nothing more to solve than the classical heat equation. In many cases, the canonical form allows a general solution by standard mathematical techniques such as separation of variables and Laplace transforms. In other cases, the general solution of the BPE is reduced to a single inverse Laplace transform.

MSC:

91B28 Finance etc. (MSC2000)
35K15 Initial value problems for second-order parabolic equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)

Software:

Algorithm 368
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References:

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