An Exposition on the Mathematics and Economics of Option Pricing

The application of options pricing theory to value irreversible investment decisions has witnessed a marked increase over the last decade. For instructional and simplified applications, the Black-Scholes model is commonly demonstrated due to its tractability and acceptance in the finance community. This paper provides a detailed mathematical exposition of the Black-Scholes model. The main contribution of this paper is the step-by-step instructional account of the Black-Scholes model that can be used directly in the classroom to introduce stochastic calculus, arbitrage-free valuation, and option-pricing theory. In contrast with most Black-Scholes derivations found in the pedagogical literature, this paper develops the fair option price from an economic equilibrium perspective. Through this approach, it is hoped the reader will comprehend both the mathematics and economics underlying option pricing theory, as both are equally important