Alternative Approach for the Derivation of Black-Scholes Partial Differential Equation in the Theory of Options Pricing Using Risk Neutral Binomial Process

Abstract

This paper presents a risk neutral binomial process as an alternative approach for the derivation of analytic pricing equation called “Black - Scholes Partial differential Equation” in the theory of option pricing. Binomial option pricing is a powerful technique that can be used to solve many complex option pricing problems. In contra st to the Black - Scholes model and other option pricing models that require solutions to stochastic differential equations, the binomial model is mathematically simple. Binomial model is based on the assumption of no arbitrage. The assumption of no arbitra ge implies that all risk - free investments earn the risk - free rate of return and no investment opportunity exists that requires zero amounts of investment but yield positive returns.