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.
Glossar
Monte Carlo Simulation
Iteration ⎊ Within cryptocurrency derivatives and options trading, iteration forms the core of a Monte Carlo Simulation, representing the repeated sampling process used to approximate probability distributions and assess risk.
Numerical Option Pricing
Methodology ⎊ Numerical option pricing encompasses a suite of computational techniques, such as finite difference methods, Monte Carlo simulation, and binomial trees, used to determine the theoretical value of derivative contracts.