Note on an Extension of an Asymptotic Expansion Scheme
AbstractThis note presents an extension of a general computational scheme of an asymptotic expansion proposed by our previous works(, , ). 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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Bibliographic InfoPaper 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.
Length: 23 pages
Date of creation: Aug 2012
Date of revision: Dec 2012
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-09-09 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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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