Option Pricing Models: The Review of Literatures

(1) Bachelier (1900) Model

Abstract

This paper reviews Bachelier (1900) and related literature up to now. Bachelier (1900) presented the first option pricing model based on his mathematical theory of Brownian motions. His model assumed that the underlying price follows the arithmetic Brownian motion that allows negative asset prices and therefore it does not satisfy no-arbitrage conditions. Samuelson (1965), Smith (1976) and others criticize these points and proposed the more general stochastic process, the Geometric Brownian motion, to overcome these problems. Later, Liu (2007) and Kolman (2013) apply the risk neutral approach to value the option whose underlying asset prices follow the arithmetic Brownian motion, but they still fall on the same problem; violation of no-arbitrage conditions. In this note, I try to propose a new pricing model to resolve this problem and extend Bachelier work based on the general equilibrium analysis, i.e. stochastic discount factor approach. Bachelier (1900) model is still useful in real option analysis and corporate finance because both types of research focus on the cash flow of projects and corporate profits which can take a negative value; i.e. losses. The many pieces of research dealing with the relationship between option and profit or project cash flow are also reviewed