Asymptotic Behaviour of The Heat Equation as The Solution of The Black-Scholes Model

Abstract

We carry out the reduction of the Black - Scholes equation via series of transformations to
obtain the heat equation by reversing the direction of time,so that the pay-off of the Black-Scholes become
the initial value condition of the heat equation.The solution of the obtained heat equation is generalized
as the solution of the Black-Scholes equation.Here we examine the 1-dimensional case and its extension
to the multi-dimensional case.