Accuracy and limitations

These figures are arithmetic, not estimation. Given your inputs, they are correct to the precision of the calculation and will not drift:

• Profit and loss at expiration at any underlying price. An option’s expiration value is defined, not modelled.
• Breakeven prices. Solved exactly from the piecewise-linear payoff, not approximated by search.
• Maximum profit and maximum loss, including the determination that one of them is unlimited.
• Net debit or credit, entry cost, and the effect of commissions and fees on all of the above.

The caveat on all four is the obvious one: they are exact for the inputs you gave. If the premium you typed is not the premium you get filled at, the exact answer is to the wrong question.

Everything that depends on what happens before expiration is a model output.

• Value on any date before expiration, including every point on the dashed line in the chart and every column in the profit table except the last.
• All five Greeks. They describe the model’s sensitivities, which approximate the market’s.
• Implied volatility solved from a premium.
• Every probability. These are the softest numbers on the site.
• Theoretical premiums, wherever a price was generated rather than entered. These carry a Model badge everywhere they appear.

Black-Scholes-Merton is a good model with specific, known-false assumptions. They are not obscure, and each one costs you in a predictable direction.

Volatility is constant across strikes

It is not. Real option chains show a volatility smile or skew: out-of-the-money puts almost always carry higher implied volatility than at-the-money options, because people pay up for crash protection. If you price a whole strategy at one volatility, the wings will be mispriced relative to the market — usually too cheap on the put side. This matters most for iron condors, strangles and anything else whose profit lives in the wings.

Volatility is constant over time

It is not. Implied volatility rises into earnings and collapses immediately after, and it rises in market stress. A long option position that looks profitable in the model can lose money on a favourable price move if volatility falls further than the move gained. The volatility slider on the calculator exists so you can test this rather than be surprised by it — move it down 10 points and see what a post-earnings crush does to your position.

You can trade continuously at one price

You cannot. Every option has a bid and an ask, and on anything but the most liquid contracts the gap between them is a meaningful fraction of the premium. A four-leg strategy crosses four spreads to open and four to close. On a wide-spread underlying that alone can exceed the maximum profit the calculator shows.

Returns are lognormally distributed

They are not. Real markets have fatter tails: large moves happen considerably more often than the model says. Every probability on this site is therefore too comforting at the extremes. When the calculator says a short strike has a 4% chance of being breached, the real figure is higher, and the difference is concentrated in exactly the scenarios that hurt.

Dividends are a smooth continuous yield

They are not. Dividends arrive on specific dates in specific amounts, and the day before an ex-dividend date is when American calls get exercised early. Modelling that as a continuous yield is a reasonable approximation for most positions and a bad one if you are short a call that is in the money going into an ex-dividend date.

Comparing this calculator against a broker platform and finding a difference does not mean one of them is broken. The usual causes, in rough order of frequency:

1. Different volatility input. Your broker uses the implied volatility derived from the live market price of each specific contract. If you typed a single volatility here, or used a theoretical premium, you are pricing a different option.
2. Different probability basis. Some platforms use delta as a rough proxy for probability of expiring in the money. Some use a risk-neutral drift, some use zero drift. These produce visibly different numbers from identical market data. Ours states its assumption beside every figure.
3. Mid price versus natural price. A quote at the midpoint of the bid-ask spread is not a price you can necessarily get filled at.
4. Trading days versus calendar days. Theta here is per calendar day. Some platforms report per trading day, which makes decay look slower than it is over a weekend.
5. American versus European pricing. A binomial model and Black-Scholes give different answers for American puts and for dividend-paying stocks.

Specific situations where the output here is materially unreliable:

• Illiquid contracts. If open interest is in single digits and the spread is 30% of the premium, the model price is a fiction. You will not trade at it.
• Anything expiring today or tomorrow. As time to expiration approaches zero, Greeks become extremely large and unstable, and small price moves produce enormous swings. The model is at its least useful precisely when the position is at its most dangerous.
• Across an earnings announcement. Implied volatility before and after earnings are effectively different regimes. A single volatility input cannot represent both, and the profit table spanning the event will be wrong on one side of it.
• Short options at risk of assignment. This calculator does not model early assignment. A short leg that gets assigned changes the position into something else entirely, and the payoff you were looking at no longer applies.
• Any position you cannot afford to be wrong about. That one is not about the model.

Stated plainly, so you know where the edges are:

• Early assignment on short options, and the position that results from it.
• Discrete dividends on specific ex-dividend dates.
• Borrow costs or hard-to-borrow fees on short stock.
• The volatility smile — one volatility applies per leg, as you set it.
• Margin requirements as your specific broker computes them.
• Taxes, including the wash sale rule and the treatment of assigned positions.
• Corporate actions: splits, mergers, special dividends and the adjustments they cause.
• Pin risk at expiration when the underlying closes at a strike.

Some of these are on the list to add. None of them are hidden. If a limitation here affects a position you are working on and you want it modelled, say so — that is how the list gets shorter.

For the formulas themselves and the reference values they are tested against, see the methodology page.