# 5. The Monte Carlo method

## Why it matters

The value of using the Monte Carlo method is in reducing uncertainty to a point where you feel comfortable enough to take a calculated risk based on likely future outcomes.

When faced with complex scenarios with uncertainty, Monte Carlo simulations beat most other approaches when it comes to estimating risk, uncertainty or schedule.

Data at NASA from over 100 space missions showed that Monte Carlo simulations beat other methods for estimating cost, schedule and risks.

## How it works

### Monte Carlo History

The Monte Carlo method was developed by Stanislaw Ulam, a mathematician who worked on the Manhattan Project together with John Von Neumann, as an approach to investigate neural diffusion.

Stanislaw got the idea when trying to predict the chance of winning the card game Solitaire. Instead of using combinatorial calculations to figure out the chance of success, he tried a different approach, simulating a number of games and observed how many actually came out successful.

### Application

Monte Carlo simulations are useful when you want to predict a target variable (such as forecasting house prices, cost, schedule, or profit) based on a number of input variables that are likely to fluctuate, i.e. carry uncertainty.

A Monte Carlo simulation repeats this sequence:

• Pull the input variables using random sampling on its respective target distribution.
• Run the input variables through a model (e.g. pricing a stock option).
• Calculate the target variable, and store it.
• Repeat hundreds or thousands of times, storing the target variable each time.

What you get in the end is a target variable distribution. In the example above, the price of a stock option, plus a confidence range. In the example of software development, the Monte Carlo method can be used to forecast the delivery date for a software project. The nice thing with the approach is that not only do you get an idea of the date, you also get a quantification of the uncertainty that comes with it.

Monte Carlo simulations would normally produce a narrower range than a traditional “what if” analysis. This is because the “what if” analysis gives equal weight to all scenarios, while the Monte Carlo simulations hardly sample in the very low probability regions (rare events).

Monte Carlo simulations have countless applications, in meteorology, astronomy, and particle physics. In finance, the Monte Carlo method is used to assess default risk and to analyze derivatives such as options.

## References

The Failure of Risk Management: Why It’s Broken and How to Fix It, Douglas W. Hubbard, Wiley 2009

The Monte Carlo Method, Wikipedia