What is the magic of Monte Carlo simulation?

Answer 1

Monte Carlo simulation is a way to add variance to a problem set. So, for instance, you are building pro forma statements for a business, and you want to know the business' sensitivity to these external forces. You'd build a model that represents your best insights into what variables drive what results (usually using regression tests). Then you run a Monte Carlo simulation with your variables subject to random events, and see how your company might fare.

Let's get concrete. If your business is a McDonalds franchise, and the corporate marketing people are running a promotion for three weeks on ice cream. You know, from past years, that your ice cream sales are dependant on the weather. So, you create a model that predicts ice cream sales based on temperature, cloudiness, and rain. Those are your input variables that were created from past regression tests. Now, you create a Monte Carlo simulation that feeds random numbers into your three variables within the limits of expected values (you set your min, max, median, standard deviation for the numbers your simulation will produce). Next, you run some tests, say 1,000 practice runs. What you get is a data set of predictions of how your McDonalds franchise might do if the weather does or does not cooperate.

The bottom line is Monte Carlo simulation takes past performance of one system and extrapolates that performance into results of another system (say weather and a company).

One simple way to do this is in Excel with the randbetween function. If I still used Excel (I've switched to OpenOffice), I'd send you a copy of my models.

There are a lot of specialized tools that are much better than Excel as well.

Finally, I understand that this is a long and narrow discussion of Monte Carlo. This is how it was explained to me in business school, and how I've applied it. There are obviously many more uses for it in science and research. There are also more mathematically grounded answers to your question.

Feel free to follow up with me through Yahoo! Answers. Email tends to work better than IM.

Good Luck

Answer 2

Magic? What "magic" are you referring to? A Monte Carlo simulation is a brute-force attempt to solve a problem or answer a question. Basically you are just trying everything possible and seeing what happens. It's kind of a trial-and-error solution when the pure mathematical solution is impossible to analyze or solve.