Option Pricing Model Comparison between Black Scholes Merton Model and Monte Carlo Simulation

Abstract

The rapid growth of global option markets underscores the importance of accurate option pricing models for effective risk management and trading strategies. This paper focuses on two cornerstone methods: the Black–Scholes–Merton (BSM) model and Monte Carlo simulation. The central question is how the analytical efficiency of the BSM model compares with the flexibility of Monte Carlo simulation when applied to standard and complex options. The paper introduces the theoretical foundations of both models, highlighting the BSM model’s closed-form precision under strict assumptions and Monte Carlo simulation’s ability to handle stochastic, path-dependent payoffs. A case study of a three-month European call option on Apple Inc. illustrates the respective strengths and limitations of the two models. The findings of this paper conclude that the Black Scholes Merton model is still the benchmark for the standard option pricing market. In contrast, the Monte Carlo simulation provides better flexibility in pricing exotic options and adapting to a more volatile market. By combining these two methods, this study provides a more robust basis for valuation and decision-making in modern finance.