Question

Please provide an example of a Monte Carlo simulation model (and explain).

Your simulation example should be able to:

1. Tackle a wide variety of problems using simulation
2. Understand the seven steps of conducting a simulation
3. Explain the advantages and disadvantages of simulation
4. Develop random number intervals and use them to generate outcomes
5. Understand alternative computer simulation packages available
6. Explain the different type of simulations
7. Explain the basic concept of simulation

Answer 1

In general terms, the Monte Carlo method (or Monte Carlo simulation) can be used to describe any technique that approximates solutions to quantitative problems through statistical sampling. As used here, 'Monte Carlo simulation' is more specifically used to describe a method for propagating (translating) uncertainties in model inputs into uncertainties in model outputs (results). Hence, it is a type of simulation that explicitly and quantitatively represents uncertainties.

A Simple Example: Rolling Dice

As a simple example of a Monte Carlo simulation, consider calculating the probability of a particular sum of the throw of two dice (with each die having values one through six). In this particular case, there are 36 combinations of dice rolls.

Based on this, you can manually compute the probability of a particular outcome. For example, there are six different ways that the dice could sum to seven. Hence, the probability of rolling seven is equal to 6 divided by 36 = 0.167.

Instead of computing the probability in this way, however, we could instead throw the dice a hundred times and record how many times each outcome occurs. If the dice totaled seven 18 times (out of 100 rolls), we would conclude that the probability of rolling seven is approximately 0.18 (18%). Obviously, the more times we rolled the dice, the less approximate our result would be. Better than rolling dice a hundred times, we can easily use a computer to simulate rolling the dice 10,000 times (or more). Because we know the probability of a particular outcome for one die (1 in 6 for all six numbers), this is simple.

How Accurate are the Results?

The accuracy of a Monte Carlo simulation is a function of the number of realizations. That is, the confidence bounds on the results can be readily computed based on the number of realizations.

How Monte Carlo Simulation Works

Monte Carlo simulation performs risk analysis by building models of possible results by substituting a range of values—a probability distribution—for any factor that has inherent uncertainty. It then calculates results over and over, each time using a different set of random values from the probability functions. Depending upon the number of uncertainties and the ranges specified for them, a Monte Carlo simulation could involve thousands or tens of thousands of recalculations before it is complete. Monte Carlo simulation produces distributions of possible outcome values.

Advantages and disadvantages of simulation

The advantage of Monte Carlo is its ability to factor in a range of values for various inputs; this is also its greatest disadvantage in the sense that assumptions need to be fair because the output is only as good as the inputs. Another great disadvantage is that the Monte Carlo simulation tends to underestimate the probability of extreme bear events like a financial crisis. In fact, experts argue that a simulation like the Monte Carlo is unable to factor in the behavioral aspects of finance and the irrationality exhibited by market participants. It is, however, a useful tool for advisors.