Monte Carlo Simulation
Using randomness to solve complex problems, from pricing derivatives to modeling risk.
What is Monte Carlo Simulation?
Monte Carlo simulation is a computational technique that uses repeated random sampling to obtain numerical results. In essence, it's about understanding the behavior of a system by simulating it a large number of times.
In quantitative finance, it's an indispensable tool. It's used to price complex "exotic" options that have no analytical solution, to estimate Value-at-Risk (VaR) for a portfolio, and to model the future performance of investment strategies. By simulating thousands of possible future scenarios, we can build a distribution of potential outcomes.
Modeling Stock Prices with GBM
A common use case is to model stock prices using Geometric Brownian Motion (GBM).
- is the stock price at time t.
- (mu) is the "drift" or expected return.
- (sigma) is the volatility.
- is a Wiener process or Brownian motion, representing randomness.
Interactive GBM Simulator
Adjust the drift and volatility to see how they affect the simulated stock price paths over one year (252 trading days).