Options numbers
Probability of profit (POP), explained
POP is a model’s estimate of the chance an option trade makes money at expiration. How Wenlo calculates it, how it relates to delta, and why a high POP can still be a poor trade.
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What POP means
Probability of profit (POP) is an estimate of the chance that an option position makes money if you hold it until expiration. It turns a set of prices and strikes into one number that is easy to compare across trades.
It is an estimate from a model, not a forecast and not a promise. It is calculated from today’s option prices, which reflect what traders expect right now. Those expectations change, and the model behind them makes simplifying assumptions about how stocks move.
How Wenlo calculates it
Wenlo’s calculator works out the position’s profit or loss at expiration for every possible stock price, then adds up the chance of each price where the position makes at least $0.01. Finishing exactly at breakeven doesn’t count as a profit.
The chances come from the Black-Scholes model: stock prices are assumed to follow a lognormal distribution whose width is set by the implied volatility (IV) you enter, and which drifts at the risk-free interest rate (less any dividend yield). This is called a risk-neutral probability. It is the probability that is consistent with today’s option prices, not an estimate of where the stock is most likely to go based on the company’s prospects.
Formula
For a single sold option, in words
Short put: POP = chance the stock finishes above (strike − premium)
Short call: POP = chance the stock finishes below (strike + premium)
For a bought option, the side flips: a long call needs the stock above strike + premium.
Three examples side by side
All three use a $100 stock, 30 days to expiration, IV of 30%, a 4% interest rate and no dividend, priced with the Black-Scholes model, before fees.
| Position | Premium | Breakeven | POP | Most you can make | Most you can lose |
|---|---|---|---|---|---|
| Sell a $95 put | $1.33 | $93.67 | 78% | $133 | $9,367 |
| Sell a $90 put | $0.40 | $89.60 | 90% | $40 | $8,960 |
| Buy a $105 call | $1.66 | $106.66 | 23% | Unlimited | $166 |
The pattern is the important part. The trades with the highest POP pay the least and risk the most. The bought call loses most of the time, but its loss is limited to what you paid and its gain has no cap. Under the model’s own assumptions, the premium is a fair price for each trade: a higher chance of a small win is balanced by a smaller chance of a much bigger loss.
POP, delta and the chance of finishing in the money
Three numbers often get mixed up:
- Delta is how much the option’s price moves for a $1 move in the stock. Its size is often used as a rough stand-in for the chance of finishing in the money. The $95 put above has a delta of about −0.25.
- Chance of finishing in the money is the model’s probability that the stock ends past the strike. For the $95 put it is about 28%.
- POP uses the breakeven instead of the strike. Because the premium moves the breakeven to $93.67, a short put can finish slightly in the money and still make money, so its POP (78%) is higher than 100% minus its chance of finishing in the money (72%).
For a bought option it works the other way: the premium pushes the breakeven further away, so POP is lower than the chance of finishing in the money. The $105 call finishes in the money about 28% of the time under the model, but makes money only about 23% of the time.
How implied volatility changes POP
Higher IV means the model expects a wider range of outcomes. For a sold option that cuts both ways: the premium is bigger, which moves the breakeven further away, but large moves through it also become more likely.
Example
The same put at higher IV
With IV at 45% instead of 30%, the 30-day $95 put on a $100 stock is worth about $2.79 and its breakeven is $92.21. Its chance of finishing in the money rises from about 28% to about 36%, and its POP falls from about 78% to about 72%. You’re paid more because the model sees more risk.
This is why comparing POP between two stocks only makes sense when you also compare their IV, and why POP can change sharply after an event such as earnings, when IV falls.
What POP leaves out
Risk
A probability is not an expected result
A trade that wins 90% of the time can still lose money over many trades if the losses are large enough. With the $90 put, one loss of a few thousand dollars can erase dozens of $40 wins. POP says nothing about how big the wins and losses are.
- It assumes you hold to expiration. Closing early, rolling or being assigned early changes the result.
- Real prices jump. The model assumes smooth, lognormal moves. Real stocks gap on news and earnings, and large moves happen more often than the model expects.
- IV changes. POP is a snapshot. Tomorrow’s IV, and therefore tomorrow’s POP, will differ.
- Fees and fills matter. The calculation uses the price you enter. Commissions and trading at the bid or ask rather than the model price both lower the real odds slightly.
Reading POP with max loss
Many investors find it useful never to read POP on its own. Put it next to the most you can make and the most you can lose, and ask whether you could live with the loss if the less likely outcome happens, including more than once in a row.
POP is also a good way to compare strikes on the same stock: moving a sold put further away raises POP and lowers the premium in a predictable way. For how the strategies themselves work, see Cash-secured puts, explained and Covered calls, explained; for how IV is judged, see IV Rank, explained.