On the derivation and solution of the black-scholes option pricing model

Abstract

The derivation and solution of the celebrated Black-Scholes Option Pricing Formula is set out in
rather more detail than has appeared in the literature so far. One problem with the Black-Scholes analysis
is that the mathematical skills required in the derivation and particularly in the solution of the model are
fairly advanced and probably unfamiliar to most economists. This paper derives the partial differential
equation for the call option price and gives full details of its solution. All the necessary mathematics are
given in three appendices. It is anticipated that the mathematical methods detailed here will be of wider
applicability in Economics and Finance.