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 This article is categorized under: Applications of Computational Statistics > Computational Finance