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. ）

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.