A New Computational Scheme for Computing Greeks by the Asymptotic Expansion Approach (Special Issue on Mathematical Finance, Published in "Asia-Pacific Financial Markets", Vol.11, 393-430, 2006. )

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.