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.
|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.|
|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)|