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Solvable Affine Term Structure Models

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  • Martino Grasselli
  • Claudio Tebaldi

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

  • Martino Grasselli & Claudio Tebaldi, 2008. "Solvable Affine Term Structure Models," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 135-153, January.
    • Handle: RePEc:bla:mathfi:v:18:y:2008:i:1:p:135-153
    DOI: 10.1111/j.1467-9965.2007.00325.x
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    References listed on IDEAS

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    1. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    2. Christian Gourieroux & Razvan Sufana, 2003. "Whishart Quadratic Term Structure Models," Working Papers 2003-50, Center for Research in Economics and Statistics.
    3. Martino Grasselli & Claudio Tebaldi, 2004. "Bond Price and Impulse Response Function for the Balduzzi, Das, Foresi and Sundaram (1996) Model," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 33(3), pages 359-374, November.
    4. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October.
    5. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
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