Options Probability of Profit: Monte Carlo Simulation Explained

Every options trade has a probability of making money. But how do you calculate it?

Most brokers show a single number — "72% POP" — next to your trade. That number comes from a model, but the model's assumptions are hidden. You don't know how it was calculated, what distribution it assumed, or how sensitive it is to changes in volatility.

Monte Carlo simulation takes a different approach. Instead of a formula, it simulates thousands of possible futures and counts how many of them are profitable. It's brute-force probability — and it's surprisingly intuitive once you see it in action.

What Is Monte Carlo Simulation?

Imagine you could rewind time and replay the next 30 days of stock market activity 5,000 times. Each replay would be slightly different — random daily returns drawn from a probability distribution based on current implied volatility.

After 5,000 replays, you count: how many ended above your breakeven? That's your probability of profit. How much did you make or lose on average? That's your expected value.

Monte Carlo simulation does exactly this, but with math instead of a time machine. It generates thousands of random price paths, evaluates your options position at expiration for each path, and aggregates the results.

Why Not Just Use Black-Scholes?

Black-Scholes gives you a theoretical probability based on a log-normal distribution. It's fast, elegant, and widely used. But it has limitations.

It assumes constant volatility. Real markets have volatility that changes — sometimes dramatically. A stock with 25% IV today might have 40% IV next week after an earnings surprise.

It assumes log-normal returns. Real stock returns have fatter tails than a log-normal distribution predicts. Crashes and melt-ups happen more often than the model expects.

It gives you one number. Monte Carlo gives you a distribution. You don't just get "72% POP" — you get the full range of outcomes: what's the median profit? What's the worst 5% scenario? What's the best case? The shape of the distribution matters as much as the center.

How OptionsLabPro's Simulator Works

The Probability & EV Calculator runs 5,000 simulated price paths for any trade setup you build. Here's what it shows you.

Probability of Profit (POP). The percentage of paths where your position finishes with a positive P&L. If 3,600 out of 5,000 paths are profitable, your POP is 72%.

Expected Value (EV). The average dollar P&L across all 5,000 paths. This is the number that tells you whether a trade is worth taking over the long run. A trade with 80% POP but deeply negative EV is a losing strategy — you win often but lose big when you lose.

Outcome distribution. A histogram showing how your P&L is distributed across all paths. Some trades have a tight cluster around breakeven. Others have a wide spread with fat tails. The shape tells you things that a single POP number can't.

Percentile breakdowns. What happens in the best 10% of scenarios? The worst 10%? The median? These percentiles help you understand the range of outcomes you're accepting.

Probability vs. Expected Value: The Critical Distinction

New traders fixate on probability of profit. Experienced traders care more about expected value.

Here's why. Consider two trades.

Trade A: 80% POP. When you win, you make $100. When you lose, you lose $500. Expected value: (0.80 × $100) + (0.20 × -$500) = $80 - $100 = -$20 per trade.

Trade B: 40% POP. When you win, you make $400. When you lose, you lose $100. Expected value: (0.40 × $400) + (0.60 × -$100) = $160 - $60 = +$100 per trade.

Trade A wins more often but loses money over time. Trade B loses more often but makes money over time. If you only looked at POP, you'd choose the wrong trade.

The Probability & EV Calculator shows you both numbers side by side, so you never fall into this trap.

Experiments to Try

The Premium Seller's Illusion

Build a short put spread (bull put spread) with a wide spread and high POP — something like 85%. Note the expected value. Now build the same spread but narrower, with 60% POP. Compare the expected values.

You'll often find that the "safer" trade has a lower or even negative expected value, while the "riskier" trade has a better risk-reward profile. This is the premium seller's illusion: high POP doesn't mean good trade.

How DTE Changes Probability

Set up a credit spread with 45 DTE and note the POP. Now change to 14 DTE with the same strikes. The POP changes — but does it go up or down?

The answer depends on where your strikes are relative to the current price and how much premium you collected. The simulator lets you test both scenarios and see the full distribution, not just the headline number.

Volatility's Impact on POP

Run the same trade at 20% IV and 40% IV. Higher IV means wider expected moves, which changes your probability of profit. For sellers (credit strategies), higher IV generally means higher premium but also wider tails — the extreme outcomes get more extreme.

Comparing Strategies Head-to-Head

Run Monte Carlo on an iron condor, then on a simple short put spread with similar capital requirements. Compare their POP, EV, and distribution shapes. Which one looks better when you see the full picture?

Reading the Results

When you run a simulation, don't just look at POP. Look at the distribution shape.

A tall, narrow peak near zero means the trade usually results in a small win or small loss. Low variance, low excitement, grind-it-out strategy.

A wide, flat distribution means outcomes are all over the place. You might make a lot or lose a lot. High variance — works if you have the bankroll to survive the losing streaks.

A peak at max profit with a long tail to the left is typical of credit strategies. You win your premium most of the time, but the losses when they come are much larger than the wins. This is where expected value becomes critical.

From Simulation to Decision

Monte Carlo simulation doesn't tell you whether to take a trade. It tells you the range of outcomes you're accepting. The decision is still yours.

But making that decision with 5,000 simulated outcomes in front of you is very different from making it with just a single POP number from your broker. You see the tails, you see the median, you see the expected value. You can compare alternatives and pick the one whose risk-reward profile matches your tolerance.

Try It Now

Open the Probability & EV Calculator and build any trade — a simple long call, a credit spread, an iron condor. Run the simulation and study the distribution. That histogram is worth more than any probability number your broker gives you.

Related Guides

• How to Calculate Probability of Profit — the math behind POP
• Iron Condor Strategy Guide — apply probability thinking to a real strategy
• Understanding Implied Volatility — the input that drives everything