Financial firms (and their regulators) often need estimates of portfolio values or of risk measures such as Value-at-risk (VaR), expected shortfall, …

• Sometimes can be calculated analytically but more usually larger players need to use simulation techniques (and possibly proxy models). Similar picture in non-financial field.
• Traditional workhorse: Monte Carlo simulation
• Basic form: (equally probable) simulations drawn randomly from relevant probability distribution characterising economic drivers impacting the portfolio payoff value
• Accuracy typically improves only at best in proportion to square root of number of simulations
• For large / complex books (especially with nested calculations), runtimes can be excessive to obtain an adequately low level of error
• Risk management (VaR-type) calculations particularly challenging as often include nesting.