This chapter explores both the theoretical and practical aspects of option pricing, focusing on the Black-Scholes model, Binomial Tree method, and the critical role of the yield curve in determining discount rates. It emphasizes advanced volatility modeling techniques, including GARCH, to capture the nonlinear and dynamic nature of financial markets. While traditional models like Black-Scholes assume constant volatility, this chapter demonstrates how integrating volatility forecasts and alternative pricing methods leads to more accurate valuations and better risk assessment. Through detailed analysis of option prices, Greeks, and sensitivity to market factors, the chapter provides a comprehensive framework for understanding and applying modern option pricing tools.