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Note on an Extension of an Asymptotic Expansion Scheme

  • Akihiko Takahashi

    (Graduate School of Economics, University of Tokyo, Tokyo)

  • Masashi Toda

    (Graduate School of Economics, University of Tokyo, Tokyo)

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    This note presents an extension of a general computational scheme of an asymptotic expansion proposed by our previous works([47], [41], [42]). In particular, through change of variable technique as well as the various ways of setting perturbation parameters in an expansion, we provide exibility of setting the benchmark distribution around which the expansion is made, and an automatic way for computation up to an arbitrary order in the expansion. For instance, we introduce new expansions so called Log-normal expansion and CEV expansion. We also show some concrete examples with numerical experiment, which implies a high order CEV expansion will produce more precise and stable approximation for option pricing under SABR model than existing approximation methods.

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    File URL: http://www.carf.e.u-tokyo.ac.jp/pdf/workingpaper/fseries/298.pdf
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    Paper provided by Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo in its series CARF F-Series with number CARF-F-286.

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    Length: 23 pages
    Date of creation: Aug 2012
    Date of revision: Dec 2012
    Handle: RePEc:cfi:fseres:cf286
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    1. Akihiko Takahashi & Kohta Takehara, 2010. "A Hybrid Asymptotic Expansion Scheme: An Application To Long-Term Currency Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(08), pages 1179-1221.
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