Monte Carlo Simulation for European Option Pricing: Methodology, Error Analysis, and Algorithmic Enhancements

This study explores the use of Monte Carlo (MC) simulation in pricing European options, with particular attention to error analysis and algorithmic efficiency. The paper begins with a review of the Black-Scholes model and its underlying assumptions. Monte Carlo simulation is then presented as a flexible alternative for valuing derivatives, especially in scenarios where analytical solutions are impractical or unavailable. The discussion includes a classification of key computational errors in MC methodsnamely statistical, discretization, and round-off errors. To improve accuracy and convergence, the paper implements variance reduction techniques, with a focus on control variates. Numerical experiments compare simulated option prices against Black-Scholes benchmark values across a range of volatility and maturity settings. The results highlight the practical effectiveness of Monte Carlo simulation and the influence of algorithmic adjustments on performance. This work contributes to the fields of financial engineering and computational finance by offering a structured evaluation of simulation methods through error decomposition and convergence diagnostics.