Option Pricing Models: The Evolution of the Black-Scholes-Merton Model

This paper focuses on the development and impact of the Black- Scholes-Merton (Black-Scholes) model in mathematical finance. It begins with an overview of the Black-Scholes model, including its foundational assumptions, the Black-Scholes equation, and its formula for pricing European options. The paper discusses the model’s significant advantages, such as its ability to estimate market volatility and provide a self-replicating hedging strategy.

It also addresses its limitations, including assumptions of constant volatility and perfect market conditions, which often do not align with real-world scenarios. Finally, this paper reviews advancements that have refined the model, including adjustments for stochastic volatility, price jumps, and market imperfections.