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A New Computational Scheme for Computing Greeks by the Asymptotic Expansion Approach
Authors:Ryosuke Matsuoka  Akihiko Takahashi  Yoshihiko Uchida
Institution:(1) 1Herrill Lynch Japan Securities Co., Ltd., Tokyo, USA;(2) Graduate School of Economics, The University of Tokyo, Tokyo, USA;(3) Graduate School of Economics, Osaka University, osaka, USA
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 European call options under general Markovian processes of underlying asset 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.
Keywords:asymptotic expansion approach  option pricing  Greeks  CEV process  Monte Carlo simulation  variance reduction method
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