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Closed Form Solutions For Quadratic And Inverse Quadratic Term Structure Models

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  • PETER LAURENCE

    (Department of Mathematics, Università di Roma 1, Piazz. Aldo Moro 2, 00185 Rome, Italy)

  • TAI-HO WANG

    (National Chung-Cheng University, 160, San-Hsing, Min-Hsiung, Chia-Yi621, Taiwan, ROC)

Abstract

We find fundamental solutions in closed form for a family of parabolic equations with two spatial variables, whose symmetry groups had been determined in an earlier paper by Finkel [12]. We show how these results can be applied in finance to yield closed form solutions for special affine and quadratic two factor term structure models as well as a new class of models with inverse square behavior. The latter can be considered a partial extension to two factors of pricing models related to the Bessel process devised by Albanese and Campolieti [3] and Albanese et al. [2]. A by-product of our results is that Lie's reduction method in this setting leads only to fundamental solutions that can be factorized as products of functions that depend jointly on time and on one spatial coordinate. Thus all the results in this paper extend immediately to n factor models.

Suggested Citation

  • Peter Laurence & Tai-Ho Wang, 2005. "Closed Form Solutions For Quadratic And Inverse Quadratic Term Structure Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(08), pages 1059-1083.
    • Handle: RePEc:wsi:ijtafx:v:08:y:2005:i:08:n:s0219024905003396
    DOI: 10.1142/S0219024905003396
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    References listed on IDEAS

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    1. Alexander Lipton, 2001. "Mathematical Methods for Foreign Exchange:A Financial Engineer's Approach," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4694, February.
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    Cited by:

    1. Wenqing Bao & ChunLi Chen & Jin E. Zhang, 2013. "Option Pricing with Lie Symmetry Analysis and Similarity Reduction Method," Papers 1311.4074, arXiv.org.
    2. Jan Baldeaux, 2011. "Exact Simulation of the 3/2 Model," Papers 1105.3297, arXiv.org, revised May 2011.

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