Options Profit Calculator

What this calculator answers

What is an option position worth when it expires, and what is it worth today? Enter one call or put, bought or sold, or pick one of 10 strategies: four vertical spreads, two straddles, two strangles, an iron condor and a covered call. At expiry the page gives the profit or loss, the break-even prices, the most the position can gain and lose, and the premium paid or received. With Value before expiry set to On it also values the position today with the Black-Scholes model, with the Greeks and the model’s chance of a profit. A chart and a table show the profit or loss across a range of stock prices. At its defaults the page works as it always has: one bought call, valued at expiry.

How to use this calculator

The calculator adds up what each option pays at the stock price you choose, less the premiums paid and plus those received.

What to enter

• Strategy: One call or put (the default) or one of the 10 strategies. Picking a strategy fills in a working example around a stock price of 100 and replaces the strike and premium fields with the ones it needs; type your own figures over it. Each name says which options are bought and which sold.
• Option type: Call (the default) or Put, for one call or put.
• Position: Buy (long), the default, or Sell (short), for one call or put.
• Strike price: the price per share at which the option lets its owner buy (a call) or sell (a put) the stock. Used by one call or put and by the covered call. Default 100.
• Premium per share: the option’s price per share. For a put it must be below the strike. Default 5.
• Stock purchase price: for the covered call, what you paid per share for the shares the call covers. The premium must be below it. Default 100.
• Strike 1 to Strike 4 and Premium 1 to Premium 4: a strategy’s options, numbered from the lowest strike up, each premium per share. Vertical spreads and strangles use Strike 1 and Strike 2 with Premium 1 and Premium 2. A straddle uses Strike 1 for its put and its call, with Premium 1 for the put and Premium 2 for the call. Only the iron condor uses Strike 3, Premium 3, Strike 4 and Premium 4. Each strike must be above the one before.
• Number of contracts: a whole number from 1 to 100,000. Default 1.
• Shares per contract: from 1 to 10,000. Default 100, the usual size of a US stock option.
• Stock price at expiry: the price the at-expiry figures use. Default 110.

Advanced options

The next eight fields sit in the closed Advanced options group. At their defaults they leave the result exactly as it would be without them.

• Value before expiry: Off (the default) or On. On values the options today with the Black-Scholes model from the next five fields, which appear only then.
• Current stock price: today’s price. Default 100.
• Days to expiry: calendar days, from 1 to 3,650; the model counts 365 a year. Default 30.
• Implied volatility: yearly, as quoted for the option, from 1% to 500%. Default 30%.
• Risk-free interest rate: yearly, from 0% to 20%. The help suggests the yield of a Treasury bill that matures near the expiry date. Default 0%, which leaves interest out.
• Dividend yield: the stock’s yearly dividends as a percent of its price. Default 0%.
• Lowest stock price shown and Highest stock price shown: the ends of the chart and the table. At 0, the default, the calculator chooses that end.

What the results mean

• Profit or loss at expiry: what the position makes or loses with the stock at the stock price at expiry. This is the headline figure.
• Profit or loss today: the model’s value of the position today less its cost (or, for a sale, what it was sold for less the cost of buying it back).
• Value of the position today: the model’s value of the options, plus for bought and minus for sold; for the covered call it includes the shares.
• Return on premium: the profit or loss at expiry as a percentage of the premium paid or received. Not shown for the covered call; a dash when the premium is 0.
• Break-even price: the stock price at expiry where the position neither gains nor loses; the lower one when there are two.
• Upper break-even price: the higher break-even of a straddle, a strangle or the iron condor.
• Move to break-even and Move to upper break-even: the percent change from the current stock price to each break-even.
• Chance of profit at expiry: the model’s probability that the stock ends where the position gains.
• Maximum gain and Maximum loss: the most the position can make and lose at expiry; either can read “Unlimited”.
• Total premium: for one option or the covered call, the premium times the contracts and the shares per contract.
• Net premium paid or Net premium received: for a strategy of several options, the premiums paid less those received, or the reverse.
• Delta, Gamma, Theta, Vega and Rho: delta is the change in value for a rise of 1 in the stock price, in shares; gamma the change in delta for that rise; theta the change as expiry comes one day closer; vega the change for a 1 point rise in implied volatility, and rho for a 1 point rise in the rate.

The rows of the model (today’s figures, the moves, the chance and the Greeks) appear only with Value before expiry set to On. The Greeks are for the whole position: each option’s Greek per share, negative for an option sold, times the contracts and the shares per contract, added up (in the covered call each share adds a delta of 1). A broker usually lists them per share for one option; to compare, divide the page’s figure by the contracts times the shares per contract. The worked examples below use these fields, and “How it’s calculated” lists the formula and its sources.

The formula

At expiry a call is worth the amount by which the stock price S exceeds the strike K, and nothing otherwise; a put is worth the amount by which the strike exceeds the stock price. That per-share value is I. A buyer gains I minus the premium q; a seller gains the premium minus I. Each figure is multiplied by the number of contracts n and the shares per contract m.

I = max(S − K, 0) (call),  I = max(K − S, 0) (put),  P = ±(I − q)·n·m,  Q = q·n·m,  B = K ± q,  r = P / Q,  P = Σ ±(Iᵢ − qᵢ)·n·m,  T = t / 365,  d₁ = ln(S₀ / K) / (σ·√T) + (R − δ + σ²/2)·√T / σ,  d₂ = d₁ − σ·√T,  V = S₀·e^(−δT)·N(d₁) − K·e^(−RT)·N(d₂) (call),  V = K·e^(−RT)·N(−d₂) − S₀·e^(−δT)·N(−d₁) (put),  P₀ = ±(V − q)·n·m,  Δ = ±e^(−δT)·N(±d₁) (upper signs for a call, lower for a put),  Γ = e^(−δT)·φ(d₁) / (S₀·σ·√T),  ν = S₀·e^(−δT)·φ(d₁)·√T / 100,  Θ = −S₀·e^(−δT)·φ(d₁)·σ / (2·365·√T) ± δ·S₀·e^(−δT)·N(±d₁) / 365 ∓ R·K·e^(−RT)·N(±d₂) / 365,  ρ = ±K·T·e^(−RT)·N(±d₂) / 100,  z = ln(S₀ / B) / (σ·√T) + (R − δ − σ²/2)·√T / σ,  p = N(z),  M = (B − S₀) / S₀

At expiry. P is the profit or loss (plus for a bought option, minus for a sold one), Q the total premium, B the break-even (strike plus premium for a call, minus for a put) and r the profit or loss as a share of the premium. For a seller, r is relative to the premium received, not a return on margin, and it falls below -100% when the loss exceeds the premium. A bought option loses at most its premium; a bought put gains the most, and a sold put loses the most, if the stock falls to zero; a sold option earns at most its premium.

Strategies. A strategy’s profit or loss is the sum of its options, each with its own strike Kᵢ, premium qᵢ and value at expiry Iᵢ, plus when bought and minus when sold. c is the net premium per share, paid (a debit) or received (a credit). The break-evens, maximum gain and maximum loss follow the Options Industry Council’s strategy pages for the vertical spreads, the straddles and strangles, the iron condor and the covered call. A bull call spread, a debit call spread, breaks even at its lower strike plus c, gains at most the gap between its strikes less c, and loses at most c.

Before expiry. With the model on, each option is valued by the Black-Scholes formula with a continuous dividend yield, as in Haugh’s Columbia University notes and the Kellogg School of Management’s D65 notes. S₀ is the current stock price, σ the implied volatility, R the rate and δ the dividend yield, as yearly decimals; T is the days t divided by 365, as Kellogg counts time. N is the standard normal distribution and φ its density. The box writes d₁ as two terms, ln(S₀/K)/(σ√T) + (R − δ + σ²/2)√T/σ, which equal the textbook [ln(S₀/K) + (R − δ + σ²/2)T]/(σ√T) and let the line wrap on a phone. V is one option’s value per share and P₀ the profit or loss today.

The Greeks. Δ, Γ, Θ, ν and ρ are the Black-Scholes Greeks per share. In the Options Industry Council’s units, theta is per day (the 365) and vega and rho per percentage point (the 100). The page shows them for the whole position.

The chance of profit. z is d₂ with the break-even B in place of the strike, and N(z) is the model’s probability that the stock ends above B, the risk-neutral probability of Sigman’s Columbia University notes. With two break-evens the page adds the chances of each stretch where the position gains. It is a model figure from the implied volatility you enter, not a forecast of what the stock will do.

The move to break-even. M is a percent change, the new value less the old divided by the old, as in Olivier’s Business Math on LibreTexts. A minus sign means the stock must fall.

Worked examples

A bought call. Buy one call contract covering 100 shares with a strike of 100 and a premium of 5. If the stock is at 120 at expiry, the profit is $1,500.00. The break-even price is $105.00, and the most the position can lose is the premium, $500.00, if the stock ends at or below the strike. The maximum gain reads “Unlimited”.

A bought put. Buy one put with a strike of 50 and a premium of 2. With the stock at 40 at expiry the put is worth 10 a share, so the profit is $800.00. The break-even is $48.00, the strike less the premium. The most it can gain is $4,800.00, if the stock falls to 0, and the most it can lose is the premium, $200.00.

A sold call. Sell one call with a strike of 100 for 5, and let the stock end at 103. The call is worth 3 a share, so you keep 5 less 3: a profit of $200.00, a return on premium of 40%. The most you can make is the premium, $500.00. The maximum loss reads “Unlimited”, since nothing caps how far the stock can rise.

Before expiry. Kellogg’s notes value a call with a strike of 50, the stock at 50, 91 days to go, 40% volatility and a 5% rate at 4.270089 a share. Buy one contract of it for 4 and set Value before expiry to On with those inputs. The position is worth $427.01 today, a profit today of $27.01. Delta is 56.446, Kellogg’s 0.564456 a share times 100 shares; theta is -$2.49 a day and vega $9.83 a volatility point. The break-even at expiry is $54.00, which the stock must rise 8% to reach, and the model’s chance of a profit at expiry is 33.62%.

A bull call spread. Take the Options Industry Council’s strikes, 60 and 65, with premiums of 3 and 1: buy the 60 call and sell the 65 call. The net premium paid is $200.00, which is also the maximum loss. The break-even is $62.00, the lower strike plus the net premium of 2, and the maximum gain is $300.00, the gap of 5 less the 2 paid, times 100 shares.

An iron condor. With the Council’s strikes, buy the 50 put for 0.50, sell the 55 put for 1.50, sell the 65 call for 1.60 and buy the 70 call for 0.60. The net premium received is $200.00, the maximum gain, kept if the stock ends between 55 and 65. The break-evens are $53.00 and $67.00, the inner strikes less and plus the net credit of 2. The maximum loss is $300.00, a gap of 5 less the 2 received.

Exercise and assignment at expiry

At expiry a call is worth something only with the stock above its strike, and a put only with the stock below it; the option is then in the money. Its owner can exercise it, buying (a call) or selling (a put) the shares at the strike, or sell it before it expires, and its seller can be assigned, that is, required to sell or buy the shares at the strike. An option that ends out of the money expires worthless, and the seller keeps the premium.

The Options Industry Council’s page on options exercise says that an expiring equity option in the money by $0.01 or more is exercised through the Options Clearing Corporation’s exercise by exception procedure unless the clearing firm instructs otherwise, so it is not strictly automatic. It also says that all standardized equity options are American-style, exercisable on any trading day, and that assignments are made at random. A seller can therefore be assigned before expiry. The calculator does not model that: it holds every option to expiry.

Reading the payoff chart

The stock price at expiry runs along the bottom and the profit or loss up the side. The line crosses zero at each break-even. Where it runs flat, the position has reached its maximum gain or loss. A line still rising at the right-hand edge means an unlimited gain, and one still falling there an unlimited loss, as for a sold call. At the left-hand edge it does not: a stock price cannot fall below 0, so a line still sloping there ends at a limit, such as a bought put’s maximum gain.

With the model on, a second line shows the profit or loss today at each stock price. It is a smooth curve, and it bends toward the expiry line as expiry nears. The Table tab of the result details lists the same figures at round stock prices, and the Lowest stock price shown and Highest stock price shown fields set the ends of both.

What the result does not include

Before expiry the figures are only as good as the model: Black-Scholes holds the volatility and the rate fixed and treats dividends as a continuous yield, not as dated payments. US stock options are American-style, while the model prices European options, which can be exercised only at expiry. Haugh’s notes point out that single-stock options are generally American, and the Options Industry Council’s page on the formula says American-style equity options are usually priced with a binomial model because of early exercise. For an option worth exercising early, the model can understate its value, and early assignment of a sold option is not modelled.

Commissions, margin requirements and taxes are not included. Strategies outside the list need each option worked out on its own and the results added together.

An uncovered (naked) call, a call sold without owning the shares, carries unlimited risk: the loss grows with every rise in the stock price, with no upper bound.