SOLVABLE AFFINE TERM STRUCTURE MODELS

Authors


  • We wish to thank the co-editor Tomas Björk and the referee for useful comments which greatly improved the final version of the paper; the usual disclaimer applies.

Address correspondence to Martino Grasselli, Departimento di Matematica Pura ed Applicata, via Trieste 63, Padova, Italy; e-mail: grassell@math.unipd.it.

Abstract

An Affine Term Structure Model (ATSM) is said to be solvable if the pricing problem has an explicit solution, i.e., the corresponding Riccati ordinary differential equations have a regular globally integrable flow. We identify the parametric restrictions which are necessary and sufficient for an ATSM with continuous paths, to be solvable in a state space inline image, where inline image, the domain of positive factors, has the geometry of a symmetric cone. This class of state spaces includes as special cases those introduced by Duffie and Kan (1996), and Wishart term structure processes discussed by Gourieroux and Sufana (2003). For all solvable models we provide the procedure to find the explicit solution of the Riccati ODE.

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