The Black-Scholes model is one of the most important frameworks in financial theory for pricing European-style options. Developed by Fischer Black, Myron Scholes, and Robert Merton in the early 1970s, it provides a closed-form solution for calculating the theoretical Fair Value of call and put options based on five key inputs: the current stock price, strike price, time to expiration, risk-free interest rate, and implied volatility.

The core formulas are: Call = S × N(d1) - K × e^-rT × N(d2) and Put = K × e^-rT × N(-d2) - S × N(-d1), where d1 = [ln(S/K) + (r + σ²/2) × T] / (σ × √T) and d2 = d1 - σ × √T. N(x) is the cumulative standard normal distribution function.

The Greeks measure how the option price changes relative to different factors. Delta measures sensitivity to the underlying price. Gamma measures the rate of change of Delta. Theta measures time decay per day. Vega measures sensitivity to a 1% change in volatility. Rho measures sensitivity to a 1% change in the risk-free rate. Together, these Greeks help traders understand and manage the risk profile of their options positions.