Historical Simulation Vs Monte Carlo Simulation

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)

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Historical Simulation Vs Monte Carlo Simulation

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Option Pricing Using Monte Carlo Simulation

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Common Probability Distributions