Asymptotic Expansion Approach in Finance (Forthcoming in “Large Deviations and Asymptotic Methods in Finance,” Springer Proceedings in Mathematics and Statistics, Vol. 110, 2015, Springer.)

Abstract

This paper provides a survey on an asymptotic expansion approach to valuation and hedging problems in finance. The asymptotic expansion is a widely applicable methodology for analytical approximations of expectations of certain Wiener functionals. Hence not only academic researchers but also practitioners have been applying the scheme to a variety of problems in finance such as pricing and hedging derivatives under high-dimensional stochastic environments. The present note gives an overview of the approach.