What Is the Difference between Analytical and Numerical Option Pricing Models?

Analytical models, like Black-Scholes, use a closed-form mathematical equation to arrive at a precise theoretical price for the option. They are fast and efficient but rely on restrictive assumptions, such as the inability to exercise early.

Numerical models, such as the Binomial Tree or Monte Carlo simulation, approximate the option's price by modeling the underlying asset's price path over time. They are slower but can handle complex features like early exercise (American options) and changing volatility more accurately.