The Black-Scholes Option Pricing Model aims to create a way to determine the value of options in financial markets. By assuming a perfect market and using arbitrage relations, the model helps verify complex mathematical models. To calculate the price of an option, the model considers the underlying financial instrument's value, which is assumed to follow a stochastic process over time. The model can be applied to both discrete and continuous time processes, with the former being useful for numerical computations. The key elements considered in the model include the stock price, option price, call option, implied volatility, and future contracts.