Monte Carlo Simulation Explained: Pricing Financial Derivatives Through Random Path Generation

Monte Carlo simulation is a widely used technique in quantitative finance for pricing derivatives when closed-form analytical solutions are unavailable. The method works by generating thousands of possible future asset price paths using the geometric Brownian motion model, computing the derivative payoff on each path, and then averaging and discounting the results. Raw Monte Carlo converges at a rate of 1/√N, meaning error reduction requires disproportionately more simulations, making variance reduction techniques such as antithetic variates and control variates essential for efficiency. For multi-asset instruments like basket options, correlated price paths can be generated using Cholesky decomposition applied to a correlation matrix. While slower than analytical methods like Black-Scholes, Monte Carlo remains the most flexible pricing approach, capable of handling complex, path-dependent derivatives.