**Quantitative Methods: Application**

**Reading 9. Common Probability Distributions**

**Learning Outcome Statements**

q. explain Monte Carlo simulation and describe its applications and limitations;

r. compare Monte Carlo simulation and historical simulation.

*CFA Curriculum, 2020, Volume 1*

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### Subject 12. Monte Carlo Simulation

When a system is too complex to be analyzed using ordinary methods, investment analysts frequently use

**Monte Carlo simulation**. Monte Carlo simulation involves trying to simulate the conditions that apply to a specific problem by generating a large number of random samples using a random number generator on a computer.After generating the data, quantities such as the mean and variance of the generated numbers can be used as estimates of the unknown parameters of the population (parameters are too complex to find through normal methods).

The term "Monte Carlo simulation" derives from the generation of a large number of random samples, such as might occur in the Monte Carlo Casino.

- It allows us to experiment with a proposed policy and assess the risks before actually implementing it. For example, it is used to simulate the interaction of pension assets and the liabilities of defined benefit pension plans.
- It is widely used to develop estimates of
**Value at Risk**(VAR). VAR involves estimating the probability that portfolio losses exceed a predefined level. - It is used to value complex securities such as European options, mortgage-backed securities with complex embedded options.
- Researchers use it to test their models and tools.

Limitations of Monte Carlo Simulation:

- It is a complement to analytical methods. It provides only statistical estimates, not exact results.
- It does not directly provide precise insights as analytical methods do. For example, it cannot reveal cause-and-effect relationships.

**Historical simulation**samples from a historical record of returns (or other underlying variables) are used to simulate a process because the historical record provides the most direct evidence on distributions (and that past applies to the future). In contrast, Monte Carlo simulation uses a random number generator with a specified distribution. A drawback is that any risk not represented in the time period selected will not be reflected in the simulation. For example, if a stock market crash did not take place in the sample period, such a risk will not be reflected in the simulation. In addition, this method does not lend itself to "what-if" analysis.###
**User Contributed Comments**
2

You need to log in first to add your comment. ###### sahilb7

Monte Carlo: Large number of random samples

Historical Simulation: Historical record of returns

###### ashish100

Damn should've just scrolled down and read sahilb7's comment instead.