A New Computational Scheme for Computing Greeks by the Asymptotic Expansion Approach ( Revised as CARF-F-044(2005); Published in "FSA Research Review", 72-108, 2005. ?

Ryosuke Matsuoka, Akihiko Takahashi and Yoshihiko Uchida
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Ryosuke Matsuoka: Graduate School of Economics, University of Tokyo
Akihiko Takahashi: Faculty of Economics, University of Tokyo
Yoshihiko Uchida: Graduate School of Economics, Osaka University

No CARF-F-033, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

Abstract: We developed a new scheme for computing "Greeks"of derivatives by an asymptotic expansion approach. In particular, we derived analytical approximation formulae for deltas and vegas of plain vanilla and average call options under general Markovian processes of underlying asset prices. We also derived approximation formulae for gammas of plain vanilla and average call options, and for deltas of digital options under CEV(Constant Elasticity of Variance) processes of underlying assets' prices. Moreover, we introduced a new variance reduction method of Monte Carlo simulations based on the asymptotic expansion scheme. Finally, several numerical examples under CEV processes confirmed the validity of our method.

Pages: 34 pages
Date: 2005-04
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Persistent link: https://EconPapers.repec.org/RePEc:cfi:fseres:cf033

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