# Monte Carlo Simulation models

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## 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, science etc.

## How does a 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.

Applications:

• 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.

What is the Monte Carlo Method?

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