The fundamental assumption of the Historical Simulations methodology is that you base your results on the past performance of your portfolio and make the assumption that the past is a good indicator of the near-future. The following is a comparison of historical simulation with Monte Carlo simulation on various factors.
| Â | Historical Simulation | Monte Carlo Simulation |
| General | Estimates prices by reliving history; we take actual historical rates and revalue a the asset each change in the market | Estimates prices by simulating random scenarios. |
| Use | Appropriate for all types of instruments, linear or non-linear | Appropriate for all types of instruments, linear or nonlinear |
| Distribution of risk factors | The historical simulation method replicates the actual distribution of risk factors. | Monte-Carlo simulation is general in nature. Â |
| Distribution Assumptions | No need to make distributional assumptions | You can use various distributional assumptions (normal, T-distribution, and so on) |
| Possibility of extreme events happening | In the case of historical simulation the possibility of extreme events happening is only more relevant if it happened in recent history. | Monte-Carlo method due to its complete random nature accounts for these events completely. |
| Disadvantage | You need a significant amount of daily rate history (at least a year, preferably much more) You need significant computational power for revaluing the portfolio under each scenario. | Takes a lot of computational power (and hence a longer time to estimate results) |