Note on an Extension of an Asymptotic Expansion Scheme (Revised in January 2013)

Abstract

This note presents an extension of a general computational scheme of an asymptotic expansion proposed by our previous works([49], [42], [43]). In particular, through change of variable technique as well as the various ways of setting perturbation parameters in an expansion, we provide exibility of setting the benchmark distribution around which the expansion is made and an automatic way for computation up to an arbitrary order in the expansion. For instance, we introduce new expansions so called Log-normal expansion and CEV expansion. We also show some concrete examples with numerical experiment, which implies a high order CEV expansion will produce more precise and stable approximation for option pricing under SABR model than existing approximation methods.