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Median outcome
$0
half end above, half below
Average (mean) outcome
$0
pulled up by lucky paths
Value at Risk (95%)
$0
potential loss vs. money invested
Expected shortfall (CVaR)
$0
average loss in the worst tail
Chance of any loss
0%
ending below what you put in
Chance of doubling
0%
ending at 2× what you put in
Median max drawdown ⓘThe typical worst peak-to-trough decline along the way, measured on year-end values. Half of simulated paths had a deeper dip, half shallower.
0%
typical worst dip en route
Sharpe ratio
0.00
(return − risk-free) ÷ volatility

Pessimistic · 5th %ile

$0

Median · 50th %ile

$0

Optimistic · 95th %ile

$0

The range of possible journeys

Each band shows where your portfolio value falls across all simulations, year by year. Half of all paths stay inside the dark band.

Where you could end up

Distribution of final portfolio values across all simulations.

Percentile table

PercentilePortfolio valueTotal returnChance of exceeding
Expected NPV (mean)
$0
average across all simulations
Median NPV
$0
the middle outcome
Probability NPV > 0
0%
chance the project creates value
NPV at risk · 5th %ile
$0
a bad-luck outcome
IRR on expected flows ⓘThe discount rate at which the expected cash flows exactly break even. If it exceeds your discount rate, the project adds value on average.
—
vs. your discount rate

NPV distribution

Outcomes left of the break-even line destroy value; outcomes to the right create it.

Monte Carlo price
$0.00
± standard error
Black-Scholes price
$0.00
exact closed-form benchmark
Chance of expiring ITM
0%
risk-neutral probability
Delta ⓘHow much the option price moves per $1 move in the stock.
0.00
per $1 stock move
Gamma ⓘHow fast delta itself changes per $1 move in the stock.
0.00
delta's rate of change
Vega ⓘHow much the option price changes for a 1-percentage-point change in implied volatility.
0.00
per 1% change in volatility

Where the stock could be at expiration

Simulated stock prices at expiry. Green bars are in the money; the option only pays off there.

Results

Mean
—
Median
—
Std deviation
—
5th percentile
—
95th percentile
—
Probability > 0
—

Outcome distribution

Distribution of your formula's result across all iterations, with the 5th, 50th and 95th percentiles marked.

How these simulations work

A Monte Carlo simulation runs your scenario thousands of times, drawing random values for the uncertain inputs each time, then studies the whole range of outcomes instead of a single guess. The portfolio tool uses a geometric model calibrated so the average yearly growth exactly matches your expected return — and values can never fall below zero, unlike simple normal-return models. Drawdowns are measured peak-to-trough within each path on year-end values, and the reported figure is the median across paths.

Value at Risk (VaR) is the loss versus the money you put in at your chosen confidence level — at 95%, only 1 in 20 simulated futures lost more. Expected shortfall (CVaR) answers the follow-up question: when things do go that badly, how bad is it on average? The options tool simulates risk-neutral price paths and reports the Monte Carlo standard error alongside the exact Black-Scholes benchmark, with analytic Greeks (delta, gamma, vega) including dividend yield.

Because the draws are random, results vary slightly between runs — that wobble is the standard error, and it shrinks as you add simulations. Enter a random seed to make runs exactly repeatable, which is the right way to compare the effect of changing one input.

Frequently asked questions

What is a Monte Carlo simulation?
It's a way of understanding uncertainty by brute force: instead of computing one "expected" answer, the computer plays out thousands of randomized futures and shows you the full distribution — the typical case, the lucky tail, and the unlucky tail. It's named after the casino, because at its heart it's organized dice-rolling.
How many simulations do I need?
10,000 is plenty for stable medians and percentiles in most cases. Extreme tail statistics (like 99% VaR) benefit from 50,000+. The precision improves with the square root of the count, so 4× the simulations only halves the noise — past a point, better inputs matter far more than more iterations.
What's the difference between VaR and expected shortfall (CVaR)?
95% VaR says "you have a 5% chance of losing more than this." Expected shortfall answers what happens inside that 5%: the average loss across the worst outcomes. CVaR is always at least as large as VaR and is considered the better measure of tail risk.
Why do my results change a little each time I run it?
Each run draws fresh random numbers, so summary statistics wobble by a small standard error. That's normal and honest — reality is uncertain too. If you want identical results every run (for example, to isolate the effect of changing one input), type anything into the random seed field.
How accurate is the Monte Carlo option price?
For European options the Black-Scholes formula is the exact answer under the same assumptions, so the tool shows both: the Monte Carlo estimate converges to Black-Scholes as simulations increase, and the ± standard error tells you how tight the estimate is. Seeing them agree is a great way to build intuition for how Monte Carlo works.
Which distribution should I pick in the custom model?
Use uniform when you only know a plausible range ("somewhere between 50 and 100"). Use normal when values cluster around a central estimate with symmetric uncertainty ("about 75, give or take 10"). Use triangular when you can name a minimum, a most-likely value, and a maximum — it's the workhorse of business-case modeling.
Can I rely on these numbers for decisions?
They're only as good as your inputs — the simulation faithfully explores the world you describe, not the real one. Use it to understand ranges, probabilities and sensitivities rather than to predict a single number, and treat it as education, not financial advice.