A Monte Carlo method is a technique that involves using random numbers and probability to solve problems. The term Monte Carlo Method was coined by S. Ulam and Nicholas Metropolis in reference to games of chance, a popular attraction in Monte Carlo, Monaco (Hoffman, 1998; Metropolis and Ulam, 1949).
Monte Carlo simulation is a method for iteratively evaluating a deterministic model using sets of random numbers as inputs. This method is often used when the model is complex, nonlinear, or involves more than just a couple uncertain parameters. A simulation can typically involve over 10,000 evaluations of the model, a task which in the past was only practical using super computers.
Monte Carlo simulation was named for Monte Carlo, Monaco, where the primary attractions are casinos containing games of chance. Games of chance such as roulette wheels, dice, and slot machines, exhibit random behavior.
The random behaviour in games of chance is similar to how Monte Carlo simulation selects variable values at random to simulate a model. When you roll a die, you know that either a 1, 2, 3, 4, 5, or 6 will come up, but you don't know which for any particular roll. It's the same with the variables that have a known range of values but an uncertain value for any particular time or event (e.g. interest rates, staffing needs, stock prices, inventory, products sold).
For each uncertain variable (one that has a range of possible values), you with our assistance, define the possible values with a probability distribution. The type of distribution we select is based on the conditions surrounding that variable.
Monte Carlo analysis has a number of advantages (Quantitative Risk Analysis by David Vose). They include:
- The distributions of the model’s variables do not have to be approximate
- Correlations and other inter-dependencies can be modelled
- The level of mathematics required to perform a Monte Carlo simulation is quite basic.
- Greater levels of precision can be achieved
- Complex mathematics can be included
- Monte Carlo simulation is widely recognised as a valid technique so its results are more likely to be accepted
- Changes to the model can be made very quickly and the results compared with previous models.
