Definition
Monte Carlo methods use random number generation to simulate thousands of possible outcomes for pricing derivatives, assessing risk, and optimizing portfolios. They are essential for pricing path-dependent options, multi-factor models, and complex structured products where closed-form solutions don't exist. Accuracy improves with more simulations but at increasing computational cost.
lightbulb Example
Pricing an Asian option (based on average price): simulate 100,000 price paths using geometric Brownian motion, calculate the average price for each path, compute the option payoff, and discount the average payoff to get the fair price.
verified_user Key Points
- Essential for complex derivative pricing
- Accuracy increases with more simulations
- Required for path-dependent options
- Computationally intensive but increasingly feasible