Simulation of random variables Monte-Carlo

Monte Carlo simulation

We can immediately say that this method is used precisely because it is simple. But no matter how simple it is, the Monte Carlo method remains a powerful tool, and also boasts some interesting properties that make it very attractive for solving various problems. Monte Carlo method refers to number of statistical methods, which in turn are used to calculate the expected values ​​of functions that cannot be integrated analytically because they do not have a closed form.

Why Monte Carlo? It allows us, using one and the same principle, to solve various kinds of problems. Monte Carlo simulations can be used in corporate finance, option pricing, and especially in portfolio management and financial planning. On the other hand, the method is limited in that it cannot account for bear markets, recessions, or other type of financial risk that may affect potential results.

Types of probability distributions

The Monte Carlo method uses different probability distributions to calculate uncertainty factors. The probability distributions correspond to various assumptions. Thus, the different nature of the data has different probabilities for different amounts.

Consider the probability distributions that are used in financial modeling.

Normal Distribution

It is symmetrical and applicable to natural laws like the height and weight of a person. Using the financial model, we determine the mean, which represents the expected value and the standard deviation. Analysts will use it to determine inflation and interest rates, fuel prices, etc.

Triangular Distribution

Using this distribution, you need to determine the minimum and maximum and most likely values. It is logical that values close to the most probable option will be more probable. Experts apply this distribution to periodic sales figures, inventory levels, and so on.

Uniform Distribution

In this distribution, the values of the variable claim a uniform probability of being included in the sample. Only the minimum and maximum need to be determined. In financial modeling, this allocation is used to determine future production costs.

Discrete Distribution

In a discrete distribution, we determine the specific probabilities of each of the values, that is, from a specific result.


  • Compared to the standard scenario Monte Carlo method, it shows us the exact combination of values ​​for each variable that contributed to a particular outcome. For example, scripting is often difficult to prepare a complete set of values ​​for all inputs.

  • The method can be easily represented graphically if required.

  • More accurate sensitivity analysis.

  • What is important – the results have probabilities.

Despite the many advantages of the method, it has not become recognizable, since this is not built into standard spreadsheets and the employee has to use certain procedures to achieve the result.

With CaseWare IDEA , you can automate absolutely all analysis procedures and build and adapt a Monte Carlo model with one click.


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