Constant elasticity of variance (CEV) option pricing model: Integration and detailed derivation

In this paper we review the renowned constant elasticity of variance (CEV) option pricing model and give the detailed derivations. There are two purposes of this article. First, we show the details of the formulae needed in deriving the option pricing and bridge the gaps in deriving the necessary formulae for the model. Second, we use a result by Feller to obtain the transition probability density function of the stock price at time T given its price at time t with t<T. In addition, some computational considerations are given for the facilitation of computing the CEV option pricing formula.