Black-Scholes-Merton Model and Extensions

What problem does it solve?

The Black-Scholes-Merton (BSM) pricing framework provides a theoretical method to value European options and understand hedging through the Greeks, while outlining the model's assumptions and extensions for dividends, early exercise, and volatility features.

Core Features & Use Cases

• Pricing formulas: European call and put prices via d1 and d2 with analytic Greeks (delta, gamma, theta, vega, rho).
• Extensions & edge cases: dividends, American options approximations, Merton jump-diffusion, and stochastic volatility to capture real-world features like dividends, early exercise, and volatility smiles.
• Use Case: educational explanation and practical pricing/hedging of stock/index options, plus exploration of implied-volatility surfaces and risk management.

Quick Start

Apply the Black-Scholes-Merton framework to price a European option given S, K, r, T, and sigma and interpret the resulting Greeks.