Computer Simulation of Stock Options: Utilizing the Black-Scholes Model

The Black-Scholes model remains a cornerstone in financial mathematics for valuing European-style op- tions, offering an analytical pricing framework based on parameters such as stock price, strike price, volatility, interest rate, and time to maturity. However, its assumptions—particularly constant volatil- ity—limit applicability in dynamic market environments. This study explores the integration of com- puter simulations, notably Monte Carlo methods, to enhance the Black-Scholes framework by modeling stochastic price movements and accommodating variable market conditions. The simulation process in- volves defining key market parameters, generating random price paths, calculating payoffs, and discount- ing to present value. Implementations using programming languages such as Python, MATLAB, and R enable flexibility, scalability, and integration with advanced techniques like artificial neural networks for efficiency. Applications span risk management, strategy optimization, financial education, and research, with future potential in quantum computing to further improve model accuracy and computational speed. The results underscore that combining the theoretical rigor of the Black-Scholes model with the adapt- ability of simulations provides a robust, dynamic tool for option pricing and financial decision-making in volatile markets.