Explain Monte Carlo simulation and what it is used for
The idea
Monte Carlo simulation generates many random draws from assumed distributions for the uncertain inputs of a model, computes the outcome for each, and uses the resulting distribution of outcomes to answer questions a single point estimate cannot. It is the standard tool where a problem has no closed-form solution — path-dependent options, retirement plans with variable spending, portfolios with many interacting risks. Its weakness is that it is only as good as the distributions and correlations assumed: it quantifies the consequences of those assumptions very precisely and says nothing about whether they are right.
A practice question
What does a Monte Carlo simulation produce?
- A single best estimate of the outcomeWhy not: A single number is what simulation exists to improve on. The distribution is what lets you say how often a result falls below some level.
- A distribution of possible outcomes from repeated random draws — correct
- A proof that the model is correctly specifiedWhy not: It assumes the specification and explores its consequences. A badly specified model simulates just as smoothly as a good one.
Running the model thousands of times over randomly drawn inputs builds up a distribution of results, which is what allows statements about probabilities rather than just a central case.
A harder one
When is Monte Carlo simulation most clearly preferable to an analytical solution?
- When the problem has no closed-form solution, such as a path-dependent option — correct
- When the inputs are known with certaintyWhy not: With no uncertainty there is nothing to draw from — every run would return the same answer.
- When speed of computation is the priorityWhy not: A closed form evaluates once; a simulation runs thousands of times. Speed is the argument against it.
Where a formula exists it is faster and exact. Simulation earns its cost when path dependence or interacting uncertainties put a closed form out of reach.
The hardest tier
A simulation of 100,000 trials produces a very precise 95th-percentile loss. What should temper confidence in it?
- The number of trials is too small to be reliableWhy not: 100,000 trials is ample for a 95th percentile. Adding more would reduce sampling noise that is already small.
- Percentiles cannot be estimated by simulationWhy not: They are among the things simulation estimates best — reading a percentile off the simulated distribution is straightforward.
- The precision reflects the assumptions, not reality, and the input distributions may be wrong — correct
More trials reduce sampling noise around the model's own answer; they do nothing about a mis-specified distribution or an underestimated correlation. Precision and accuracy are not the same thing.
In the app: 9 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
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