Normal approximation for call function via Stein's method

Abstract

A call function is an important tool in nance. One uses this function to compute a payo from investment. In this work, we are attentive to approximate the call function by dividing this work into three parts. First, we give uniform and non-uniform bounds on normal approximation for the call function without correction term. Second, we improve and nd the explicit constants of a bound on normal approximation for the call function with a correction term proposed by Karoui and Jiao in 2009. Third, we propose uniform and non-uniform bounds of such approximation. In the part of non-uniform bounds we present both polynomial and exponential non-uniform bounds. Our techniques are Stein's method and the zero bias transformation.