%0 Journal Article
%T Can there be an explicit formula for implied volatility?
%A Stefan Gerhold
%J Quantitative Finance
%D 2012
%I arXiv
%X It is "well known" that there is no explicit expression for the Black-Scholes implied volatility. We prove that, as a function of underlying, strike, and call price, implied volatility does not belong to the class of D-finite functions. This does not rule out all explicit expressions, but shows that implied volatility does not belong to a certain large class, which contains many elementary functions and classical special functions.
%U http://arxiv.org/abs/1211.4978v1