How Monte Carlo simulation works

Closed-form models like Black-76 handle vanilla options, but path-dependent and multi-asset payoffs, Asian options, spread options, storage and transport optionality, have no simple formula. Monte Carlo simulation is the general-purpose answer.

1. Model the dynamics: choose how prices evolve (drift, volatility, correlations between factors).
2. Simulate paths: generate thousands of random price paths consistent with those dynamics.
3. Revalue: compute the payoff of the position under each path.
4. Aggregate: average the payoffs (for a price) or read a percentile (for VaR).

Monte Carlo error shrinks with the square root of the number of paths, so ten times the accuracy costs a hundred times the paths. Variance-reduction techniques and efficient revaluation matter, which is why simulation belongs in a platform engine, not a spreadsheet.

Monte Carlo runs against the same governed positions and market data as the rest of valuation and risk, so simulated results are consistent with the book rather than a separate, un-reconciled calculation.