Lessons

- What is a Probability Distribution
- Discrete Vs. Continuous Random Variable
- Cumulative Distribution Function
- Discrete Uniform Random Variable
- Bernoulli and Binomial Distribution
- Stock Price Movement Using a Binomial Tree
- Tracking Error and Tracking Risk
- Continuous Uniform Distribution
- Normal Distribution
- Univariate Vs. Multivariate Distribution
- Confidence Intervals for a Normal Distribution
- Standard Normal Distribution
- Calculating Probabilities Using Standard Normal Distribution
- Shortfall Risk
- Safety-first Ratio
- Lognormal Distribution and Stock Prices
- Discretely Compounded Rate of Return
- Continuously Compounded Rate of Return
- Option Pricing Using Monte Carlo Simulation
- Historical Simulation Vs Monte Carlo Simulation

# 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) |