Contrast the Monte Carlo approach to simulation with the historical approach

Historical simulation generates scenarios by randomly resampling actual past returns, often whole cross-sections of dates with replacement, a bootstrap. It keeps the real data's fat tails and cross-asset correlations without having to model them, but it can only produce outcomes built from the past and assumes the sampled history is representative. Monte Carlo simulation instead draws from a specified statistical model, such as a multivariate normal or a fat-tailed distribution, with parameters estimated from data or set by judgement. It can generate outcomes never observed and test hypothetical conditions, but results are only as good as the model chosen. The trap is believing historical simulation is assumption-free: it assumes the future resembles the sampled past.