Options Payoff Calculator & Strategy Builder

How option payoffs work

At expiration a call’s intrinsic value is the greater of the underlying price minus the strike, or zero. A put’s intrinsic value is the greater of the strike minus the underlying price, or zero. A long option’s result is that intrinsic value minus the premium you typed, multiplied by the contracts and the multiplier. A short option starts from the premium and subtracts the intrinsic value. The strategy result adds the legs and then subtracts the fees once.

Premium debits and credits

The premium field is a price per underlying unit. The cash amount is that price times the quantity times the multiplier. A long option pays the premium. A short option receives it. The net of those cash amounts is a debit or a credit. A credit is money taken in at the start. It becomes a profit only after the expiration result, including every short option and any shares, is known. A debit is money paid at the start. For a long option held alone it is also the most that option can lose at expiration. A short option can lose more than the debit or the credit of the whole strategy.

Maximum profit and maximum loss

The bounds are read from the payoff on every underlying price from zero upward, including the tails beyond the chart. A finite best or worst result is the highest or lowest value at the strike knots and at a zero price. If the slope above the highest strike still rises, the profit is unbounded under the payoff model. If that slope still falls, the loss is unbounded under the payoff model. An uncovered short call has that rising loss. A short put’s loss stops at a zero underlying price in this model, so the loss is large and finite. Editing a quantity can remove a cap that a template had when you first loaded it.

Break-even analysis

A break-even is an underlying price where the strategy result is zero. The premium moves that price away from the strike. A long call struck at 100 and bought for 5 per unit breaks even at 105, because the 5 points of intrinsic value repay the premium. A spread or a straddle can have more than one break-even, or none, once the legs and the fees are combined. The roots are solved on each interval between strikes, so a root between two strikes is kept even when the chart step would have stepped over it.

Multi-leg strategies

Each template fills the leg table. After that, the result follows the legs you leave in the table. A vertical spread uses the same right and the same expiration at two strikes. A straddle uses a call and a put at one strike. A strangle uses a call and a put at different strikes. An iron condor combines a put spread and a call spread. A covered call pairs long shares with a short call. A protective put pairs long shares with a long put. Shares use an entry price and a share quantity. They are not multiplied again by an option multiplier.

Greeks explained

Delta, gamma, theta, vega and rho are local sensitivities of the Black–Scholes–Merton price. Delta is the change for a one-point move in the underlying. Gamma is the change in delta for that move. Theta is shown per calendar day. Vega is shown per 1 percentage point of volatility. Rho is shown per 1 percentage point of the interest rate. The figure on screen is the sum across the position, with a short leg carrying the opposite sign and each option scaled by its quantity and multiplier. A stock leg contributes one delta per share and zero for the other Greeks. These are model slopes at the inputs you typed. They are not a promise of the next price change.

Implied volatility

In a market, implied volatility is the volatility that makes a pricing model match an observed option price. This page does not read an option chain, so the volatility field is an assumption you supply. Raising it raises the model price of a long option in the usual European formula, and it changes the modelled result relative to the premium you typed. That column is separate from the expiration profit, which ignores volatility because the option is then worth only its intrinsic value.

Time decay

Before expiration, the model price includes time. Shortening the days remaining changes that price. Theta describes the slope of the model price as time passes, holding the other inputs still. Price, volatility and time move together in a market, so a one-column time table does not describe the whole position. At expiration the theoretical value collapses to intrinsic value, which is the payoff chart.

Strategy structures

A long call gains at expiration only after the underlying has risen enough to cover the premium. A long put needs a fall large enough to cover its premium. A covered call keeps share exposure and sells a call against it, so gains above the call strike are given up if the call finishes in the money. A protective put keeps the shares and adds a put, so the put premium is the cost of that cover until the put expires. A vertical spread pairs two options of the same right and expiration at different strikes. A ratio spread adds an extra short option, and a call ratio then has an unbounded upside loss in this model. Loading a structure is a way to fill the legs. It is not a statement that the structure suits a particular account.

Common mistakes

• Reading the premium per unit as the cash cost. The cash cost multiplies by the quantity and the multiplier.
• Leaving the multiplier at 100 when the contract specifies a different number.
• Leaving out assignment on a short option. Exercise can create a share position this chart does not open.
• Treating the premium paid as the maximum loss after a short leg or a share leg has been added.
• Reading the expiration chart as the value of the option next week. The theoretical section is the separate model for that.
• Ignoring the bid and the ask. The premium you type is a single number, and a fill can be worse.
• Leaving fees at zero when the account would charge them. Fees are subtracted once from the result.
• Assuming every contract settles the same way. The multiplier and the expiration label are yours to match the contract.
• Giving two option legs different expiration labels. The page then stops the expiration chart and the theoretical price, because one expiration’s intrinsic value does not belong on the other leg.

Risks this chart does not remove

A buyer can lose the entire premium. An uncovered short call can lose without a finite cap if the underlying keeps rising. A short put can lose a large amount as the underlying falls. A spread can be assigned on the short leg before expiration, and the two legs may not fill together at the premiums you typed. Margin is set by the broker and the contract. This page does not calculate a margin requirement from the payoff. American-style options can be exercised early. Exercise and assignment can leave shares. Liquidity and the bid-ask spread change the result you can actually trade. A change in volatility changes the model price before expiration. The expiration chart leaves out the path the price takes to get there.

The futures margin calculator uses margin amounts you type for a futures contract. Those amounts are not an options margin.

Worked example

The desk opens on a long call. The strike is 100, the premium is 5 per underlying unit, the quantity is 1 and the multiplier is 100. At an expiration price of 110 the premium paid is 500. The call’s intrinsic value is 10 per unit, so the option position is worth 1,000 before the premium is subtracted. The strategy result is +500. The break-even is 105. The maximum loss is 500. The maximum profit is unbounded under the payoff model, because the call keeps gaining as the underlying price rises. The 1,000 is the intrinsic cash value. The 500 is the result after the premium.

Assumptions and limitations

The workspace builds a strategy from calls, puts and, where you add them, shares. The expiration chart uses intrinsic value at a price you choose. A separate section prices European options with Black–Scholes–Merton from a volatility, a rate and a dividend yield you type. Premiums, strikes and the multiplier are yours. The page does not load an option chain.

How the calculation works

A call’s intrinsic value is the greater of the underlying price minus the strike, or zero. A put’s intrinsic value is the greater of the strike minus the price, or zero. A long leg subtracts the premium you typed. A short leg starts from that premium and subtracts the intrinsic value. Each option result is multiplied by its own quantity and its own multiplier. A share leg uses the share quantity and the entry price, and it is not passed through the option multiplier. Fees on the legs are subtracted once. The maximum and the break-evens are solved on the intervals between strikes across every price from zero upward. If the slope above the highest strike is still rising or falling, the profit or the loss is labelled unbounded under the payoff model. The theoretical value uses the European formula and is kept in its own column.

Assumptions

• Expiration payoff uses intrinsic value. It leaves out early exercise.
• The premium is per underlying unit. Cash premium multiplies by quantity and by the multiplier.
• The multiplier is the contract’s. One hundred is only the opening illustration.
• Every option leg in one expiration chart shares one expiration label. Different labels stop the chart.
• Volatility, the interest rate and the dividend yield are assumptions you type. They are not a reading from an option chain.
• The selected expiration price is an illustration you chose.

A worked example

One long call, strike 100, premium 5 per unit, one contract, multiplier 100, expiration price 110 and no fee. Premium paid is 500. Intrinsic value is 10 per unit, so the option is worth 1,000 before the premium. The strategy result is 500. The break-even is 105. The maximum loss is 500. The maximum profit is unbounded under the payoff model as the underlying price rises. The 1,000 is the intrinsic cash value. The 500 is the result after the premium.

Limitations

The theoretical price is a European model value. It is not an American price, an early-exercise value, or a quote a market would trade. Margin is set by the broker and is not derived from the payoff. A short call can lose without a finite cap. Two legs with different expiration labels are refused rather than priced as if they expired together. Dividends enter the theoretical model only as the continuous yield you type.

Change one input at a time if a result looks surprising. The arithmetic is only as careful as the numbers you type, and it does not know your broker’s contract size.

Options Payoff Calculator & Strategy Builder recalculates as you type. Reset restores the starting figures on that page. Those figures are an illustration of the arithmetic, not a market observation and not a record of anyone’s account. Copy and export repeat the same rounded results. Cash amounts on screen are shown to two decimal places. A conversion, a margin schedule, or a programme rule that you leave blank is not invented. A zero divisor, a stop on the wrong side of an entry, or a target-weight total other than 100 percent produces a written explanation instead of a blank or infinite number.