Monte Carlo Simulation for European Option Pricing

Monte Carlo simulation is a widely used method for pricing European options. Although this approach may not achieve the highest precision, it offers advantages in terms of speed and computational efficiency. The method works by simulating random walks of stock prices to calculate option values, making it applicable to various financial markets. By generating numerous price paths through random number generation and applying the Black-Scholes framework, we can estimate the option's payoff distribution. Key implementation steps include: 1. Simulating asset price paths using geometric Brownian motion 2. Calculating option payoffs at expiration for each path 3. Discounting the average payoff back to present value The accuracy can be improved by increasing the number of simulations, typically implemented through iterative loops that enhance statistical reliability. This approach provides flexible pricing for complex options where analytical solutions may not exist.