"The first and most important thing to understand about Monte Carlo is that it is a numerical technique, not a model."
If you ever hear people talking authoritatively about their powerful "Monte Carlo model," be very suspicious of the message and the messenger. The Monte Carlo numerical method (in contrast to the lovely place on the French Riviera) is no more a "model" than addition is a "model" for ascertaining that two plus two equals four. It is simply a way to perform certain calculations. For any lingering Pythagoreans out there, Monte Carlo is specifically a very efficient way to calculate integrals in high dimensional spaces. In finance, Markov chain Monte Carlo is used for generating estimated distributions for things like interest rates, equity prices, investment returns, and exchange rates. People who think the Monte Carlo technique is a "model" are confused. My hope is this quick post clears that up and convinces you the distinction is important.
The simple fact of the matter is that once we face a situation that involves more than about three risk factors, Monte Carlo methods are the best we've got for calculating statistics of interest. Modern homo sapiens, with our flat screen TVs, computers, multi-tasking cell phones, ipads, and big brains have simply not invented anything better than Monte Carlo to evaluate these types of problems. And the more complicated the analysis, the more factors to analyze, and the better Monte Carlo does relative to other approaches. Without getting bogged down in only mildly relevant detail, this is a direct result of Monte Carlo's uniquely wonderful properties in the face of the curse of dimensionality.
So what? Why should you care? If you're like me, you hear people periodically either dismissing outright the utility of "Monte Carlo models," or alternatively gushing about how amazingly well their "Monte Carlo model" predicts the future. When you hear this now you can rest comfortably in your understanding of the much more moderate truth: neither the naysayers nor the chest thumpers are in a position to properly use Monte Carlo to help make better financial decisions. And properly used, Monte Carlo can absolutely help inform difficult financial decisions. To that end, I leave you with a quote from Mr. Black Swan himself.
Nassim Taleb, Fooled by Randomness
"The dividend of the computer revolution to us did not come in the flooding of self-perpetuating email messages and access to chat rooms; it was in the sudden availability of fast processors capable of generating a million sample paths per minute."