Monte Carlo simulation
Estimate model quantities through repeated random sampling
Monte Carlo simulation estimates quantities by repeated random sampling from a specified model. Financial applications include derivative valuation and loss distributions; methodological research also uses it to examine estimator behaviour under known data-generating processes. Simulation error decreases with replication under appropriate conditions, but more draws do not correct a misspecified model or biased numerical discretisation.
Choose this when an expectation, distribution or estimator property is difficult to calculate analytically but a credible simulation mechanism exists. Define the target quantity and acceptable numerical uncertainty before choosing replication effort.
Strengths
- Handles complex nonlinear functions and dependence structures
- Quantifies numerical uncertainty and supports controlled sensitivity experiments
Limitations
- Rare events can require specialised sampling
- Model error and discretisation bias survive increased replication
Know the boundary
A large number of simulated paths does not make an assumed model empirically true or eliminate approximation bias.