The CEV Model Revisited

Abstract

This note introduces a mathematically rigorous short time approximation of the transition density function of the CEV model. We first apply a change of variable to the CEV operator and transform it to a Schrodinger operator with an inverse square potential, and then construct a Neumann series to the new opeator under weighted Sobolev spaces. To the author’s knowledge, this is the first time that a mathematically rigorous construction for the CEV model is obtained in the financial mathematics literature.