Higher-order asymptotics in finance

A primary motivation of higher-order asymptotic statistical analysis is to improve the first-order limiting result in accordance with the celebrated Central Limit Theorem in the sense that a better approximation with higher order accuracy can be attained. In this article, several important tools in asymptotic analysis for obtaining higher-order approximations, including Edgeworth expansions, saddle-point approximations and Laplace integral method, will be revisited together with an introduction of some of their applications in finance. A new result on bounds for the difference between American and European calls on small dividend paying stock is also provided. WIREs Comput Stat 2012, 4:571-587. doi: 10.1002/wics.1234