Derivatives Pricing: Black-Scholes, Real Options, and Market Completeness

Abstract

Options and derivatives pricing have produced some of financial economics’ most elegant theoretical achievements, most consequential practical applications, and most spectacular market failures. Black, Scholes (1973) and Merton’s (1973) option pricing formula—published simultaneously in the Journal of Political Economy and the Bell Journal of Economics—established a no-arbitrage pricing framework that earned Scholes and Merton the 1997 Nobel Prize in Economics and gave practitioners a widely used tool for pricing options, hedging risk, and valuing financial guarantees. The model’s assumptions—constant volatility, log-normal returns, continuous trading—have been systematically relaxed to address the ‘volatility smile’ (implied volatility varying with strike price), heavy-tailed return distributions, and stochastic volatility that actual markets exhibit. Real options analysis—applying option pricing theory to capital investment decisions—has extended derivative theory to the valuation of strategic flexibility in corporate investment. This paper reviews option pricing theory, the Black-Scholes formula and its limitations, stochastic volatility models, and real options applications.