CIRJE-F-366. Matsuoka, Ryosuke, Akihiko Takahashi and Yoshihiko Uchida,"A New Computational Scheme for Computing Greeks by the Asymptotic Expansion Approach", September 2005.

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 av-erage 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 con?rmed the validity of our method.