The Black-Scholes Option Pricing Model

Abstract

This chapter introduces the reader to the Black-Scholes -Merton model by identifying its assumptions and illustrating its mathematical derivation using intuitive financial reasoning. Numerical examples are also presented to help the reader understand practical aspects of this celebrated model. The analytical power of the Black-Scholes-Merton model comes from the brilliant assumption that the returns of the underlying asset follow an Ito process. This assumption allowed financial theorists to use financial reasoning with an extensive inventory of mathematical techniques to solve successfully for the pricing of contingent claims. Unlike many other scientific discoveries that are not often easily modified, the Black-Scholes-Merton model has been successfully extended and adapted to numerous underlying assets, thus offering pricing solutions as benchmark prices. This in turn has encouraged the development and implementation of numerous trading strategies that involved hedging, speculation and arbitrage.

Keywords: Black-Scholes Option Pricing, Options

JEL Classification: G10, G13