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Monte Carlo Simulation

What is Monte Carlo Simulation?

Also referred to as probability simulation or Monte Carlo method, Monte Carlo simulations are used to model the probability of different outcomes in a process that cannot easily be predicted due to the intervention of random variables. It is used to further understand the impact of risk and uncertainty in prediction and forecasting models. They can be used to tackle a great range of problems such as areas in engineering, finance and science.

The method was invented by John von Neumann and Stanislaw Ulam during the Second World War to improve decision making under certain conditions. It was named after Monaco, known for being a famous casino town at the time, given that the element of chance is central to the modeling approach, akin to a game of roulette. However, since its introduction, Monte Carlo Simulations have assessed the impact of risk in countless real-life scenarios, such as artificial intelligence, stock prices, sales forecasting, project management, and pricing. Additionally, they provide numerous advantages over predictive models with fixed inputs. For example, Monte Carlo Models are able to conduct sensitivity analysis or calculate the correlation of inputs. Indeed, sensitivity analysis allows decision-makers to see the impact of individual inputs on a particular outcome and correlation helps them to grasp the different relationships between any input variables.

How does Monte Carlo Simulation Work?

Monte Carlo simulation carries out risk analysis by building models of possible results. It does this by substituting a range of values (a probability distribution) for any factor that incorporates uncertainty. Then, it calculates results several times, while using a different set of random values from the probability functions each time. A Monte Carlo simulation could involve thousands of recalculations before it is complete, depending on the amount of uncertainties and the ranges specified for them. The simulation produces distributions of possible outcome values.

As a result of using probability distributions, variables can have different probabilities of different outcomes occurring. Probability distributions are a much more realistic way of describing uncertainty in variables of a risk analysis.

How to use Monte Carlo Methods

Monte Carlo techniques involve three basic steps:

  1. Set up the predictive model, identifying both the dependent variable to be forecasted and the independent variables that will determine the prediction (these are known as the input, risk or predictor variables).

  2. Postulate probability distributions of the independent variables. Use historical data and/or the analyst’s subjective judgment to define a range of probable values and ascribe likelihood weights for each.

  3. Run simulations repeatedly, generating random values of the independent variables. Repeat this until you can make up a representative sample of the near infinite number of possible combinations from your results


In Finance: Monte Carlo is used in corporate finance to model components of project cash flow, which are impacted by uncertainty. It is also used for option pricing, pricing fixed income securities and interest rate derivatives. However, it is more extensively used in portfolio management and personal financial planning.

Portfolio Management: Monte Carlo allows an analyst to determine the portfolio size required at retirement to support the desired retirement lifestyle and other desired gifts and bequests. It factors in a distribution of reinvestment rates, inflation rates, asset class returns, tax rates and even possible life spans. The result is a distribution of portfolio sizes with the probabilities of supporting the client's desired spending needs.

To learn more about Monte Carlo Simulation

Introduction to Monte Carlo Methods

Monte Carlo Simulation

Advantages and disadvantages

What is the Monte Carlo Method?

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