What is Monte Carlo Simulation? (And Why Finance Needs It)

Let's get one thing out of the way: Monte Carlo simulation is named after a casino. That should tell you everything about what it does — it's about probability, randomness, and understanding the range of things that could happen.

In finance, it's one of the most underused tools that exists. And once you understand it, you'll never look at a single-point DCF the same way again.

The Problem With Single Scenarios

When you build a standard DCF, you plug in one growth rate, one discount rate, one terminal growth rate, and you get one intrinsic value. Then you present it with false precision: "The stock is worth $142.37."

But you know that growth won't be exactly 8%. WACC won't be exactly 10%. Terminal growth won't be exactly 2.5%. Every input is an estimate, and small changes in estimates produce massive changes in output. A sensitivity table helps, but it only shows you a grid — it doesn't tell you the probability of each outcome.

Monte Carlo simulation fixes this by asking a better question: "Given the uncertainty in my assumptions, what's the distribution of possible outcomes?"

How It Actually Works

The concept is beautifully simple:

Define ranges for your inputs. Instead of "growth rate = 8%," you say "growth rate follows a normal distribution with mean 8% and standard deviation 3%." This captures the uncertainty.

Run the model thousands of times. Each run randomly samples from those distributions. Run 1 might use 6.2% growth, 9.8% WACC. Run 2 might use 11.4% growth, 10.3% WACC. Each combination produces a different valuation.

Analyze the distribution. After 10,000 runs, you have 10,000 different valuations. Plot them as a histogram. Now you can say things like: "There's a 70% probability the stock is worth between $110 and $175" instead of "the stock is worth $142.37."

That's it. That's Monte Carlo. Run the model a lot of times with random inputs and look at the distribution of results.

Why It Matters in Finance

It quantifies uncertainty

A standard DCF gives you a point estimate. A Monte Carlo DCF gives you a probability distribution. The difference is enormous.

Imagine two companies both valued at $100/share by a standard DCF. Company A's Monte Carlo shows a tight distribution — 90% of outcomes fall between $85 and $115. Company B shows a wide distribution — 90% of outcomes fall between $40 and $200.

Same expected value, completely different risk profiles. The single-scenario DCF hides this.

It kills false precision

Nothing in finance is more dangerous than a precise number derived from uncertain inputs. When your DCF says "$142.37/share," there's an implicit claim of precision that doesn't exist. Monte Carlo forces honesty by showing the full range of outcomes.

It helps with decision-making

"There's a 65% chance the stock is undervalued at the current price" is far more useful for decision-making than "my DCF says it's worth $142.37." The first statement acknowledges uncertainty. The second pretends it doesn't exist.

The Math (Not as Scary as You Think)

The most common approach uses a random number generator that samples from probability distributions:

Normal distribution — for inputs like growth rates and margins that cluster around an average. Most outcomes are near the mean, with extreme values being rare.

Log-normal distribution — for stock prices and market values that can't go below zero. This is what the Black-Scholes model uses.

Uniform distribution — when you genuinely have no idea and just want to say "somewhere between X and Y with equal probability."

For each simulation run, you sample each input from its distribution, run the model math (same formulas as a normal DCF), and record the output. After thousands of runs, you analyze the results.

The key insight is that the random number generator does the hard work. The model itself is identical to a regular DCF — you're just running it 10,000 times with different inputs each time.

Where Monte Carlo Shows Up

Valuation — Monte Carlo DCF produces a probability distribution of fair value instead of a point estimate. This is what Prova's Monte Carlo DCF model does.

Retirement planning — Will your savings last 30 years? Depends on market returns, which are uncertain. Monte Carlo simulates thousands of possible market paths — bull markets, crashes, flat decades — to calculate the probability your money lasts. Prova's Monte Carlo Retirement model does exactly this.

Portfolio risk — VaR (Value at Risk) calculations at major banks are Monte Carlo simulations. What's the worst-case loss at a 95% confidence level?

Options pricing — When analytical solutions don't exist (exotic options, path-dependent payoffs), Monte Carlo is the standard approach.

Project finance — will the oil field / renewable energy project / infrastructure investment generate sufficient returns under various commodity price scenarios?

A Quick Example

Say you're valuing a company with a standard DCF:

Revenue growth: 8% (but could realistically be 3-13%)

EBITDA margin: 25% (but could be 20-30%)

WACC: 10% (but could be 8-12%)

Terminal growth: 2.5% (but could be 1.5-3.5%)

Your point-estimate DCF gives you $50/share. Helpful, but limited.

Now run a Monte Carlo with 10,000 iterations. The results might show:

Median value: $48/share

10th percentile: $28/share (10% chance it's worth less than this)

90th percentile: $78/share (10% chance it's worth more than this)

Probability stock is undervalued at $40: 62%

Now you have something you can actually use for decision-making.

Common Misconceptions

"It's only for quants." Nope. If you can build a DCF, you can run a Monte Carlo. The math is the same — you just run it more times.

"More simulations = more accurate." Not exactly. Going from 100 to 1,000 simulations helps a lot. Going from 10,000 to 100,000 barely changes the distribution. 10,000 is the sweet spot.

"It gives you the right answer." It doesn't. It gives you the distribution of possible answers given your assumptions. If your assumptions about the input ranges are wrong, the output distribution will be wrong too. Garbage in, garbage out — just with more statistical confidence.

"It's computationally expensive." In the 1990s, yes. In 2026, running 10,000 DCF simulations takes about 2 seconds in your browser. Not exactly a supercomputer problem.

Try It Yourself

Prova has two Monte Carlo models you can run for free:

Monte Carlo DCF — probabilistic valuation with stochastic revenue, margins, and discount rates. See the distribution of possible fair values for any public company.

Monte Carlo Retirement — stress-test your retirement plan across 10,000 market scenarios. Find out the probability your savings actually last.

Run a Monte Carlo DCF | Run a Monte Carlo Retirement