A Complete Market Model for Option Valuation

Abstract

This paper is an introduction and survey of Black-Scholes Model as a complete model for Option Valuation. It is a Stochastic processes that represent diffusive dynamics, a common and improved modelling assumption for financial systems.

As the markets are frictionless generally, it becomes very necessary for us to use a more convenient and complete method in order to avoid errors for computations. We include a review of Stochastic Differential equations(SDE), the -lemma which gives a clear picture of Log-normal distribution of a Geometrical Brownian Motion path and solution of Black- Scholes  Model

Keywords: Stochastic Differential Equations, ’s lemma, tame and completeness of Black-Scholes Model