Solvable Affine Term Structure Models

19 Pages Posted: 19 Dec 2007

See all articles by Martino Grasselli

Martino Grasselli

University of Padova - Department of Mathematics; Léonard de Vinci Pôle Universitaire, Research Center

Claudio Tebaldi

Bocconi University - CAREFIN - Centre for Applied Research in Finance; Bocconi University - Department of Finance; Bocconi University - IGIER - Innocenzo Gasparini Institute for Economic Research

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, where 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.

Suggested Citation

Grasselli, Martino and Tebaldi, Claudio, Solvable Affine Term Structure Models. Mathematical Finance, Vol. 18, Issue 1, pp. 135-153, January 2008, Available at SSRN: https://ssrn.com/abstract=1073259 or http://dx.doi.org/10.1111/j.1467-9965.2007.00325.x

Martino Grasselli (Contact Author)

University of Padova - Department of Mathematics ( email )

Via Trieste 63
Padova, Padova
Italy

Léonard de Vinci Pôle Universitaire, Research Center ( email )

Paris La Défense
France

Claudio Tebaldi

Bocconi University - CAREFIN - Centre for Applied Research in Finance ( email )

Via Roentgen 1
Milan, 20136
Italy

Bocconi University - Department of Finance ( email )

Via Roentgen 1
Milano, MI 20136
Italy

Bocconi University - IGIER - Innocenzo Gasparini Institute for Economic Research ( email )

Via Roentgen 1
Milan, 20136
Italy

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