Before you buy or sell an option, you use its profit or loss at expiry to check the result at each price at expiry and how far a loss can extend.

Profit or loss is the payoff minus the premium

The payoff of an option is the amount gained by exercising it at expiry, and it is zero when the option is not exercised. The buyer's profit or loss at expiry is this payoff minus the option premium paid at the start of the trade1. How a call option (call) and a put option (put) work is covered in Option Basics: Calls and Puts. Buying or selling a call and buying or selling a put give four positions.

Consider a hypothetical example in which you buy one unit of a call, the right to buy the underlying asset at a strike price of 100 yen, for a premium of 5 yen. If the price at expiry is above the strike price, the buyer exercises the right, buys the underlying for 100 yen, sells it at the market price, and keeps the difference. If the price is below the strike price, the buyer lets the right lapse2. The payoff and profit or loss at each price at expiry are as follows.

Price of the underlying at expiry (yen) Payoff (yen) Premium (yen) Profit or loss (yen)
80 0 −5 −5
100 0 −5 −5
105 5 −5 0
110 10 −5 5
120 20 −5 15

The buyer's payoff never falls below zero. The profit or loss, however, is always lower than the payoff by the 5 yen premium. At any price of 100 yen or less at expiry, the buyer loses 5 yen. In this example, the gap in time between paying the premium and expiry (and the interest over that period), trading fees, and taxes are ignored, and the premium is subtracted as it is. Sources do not use the terms payoff and profit or loss consistently, and some call a line drawn without subtracting the premium a "profit and loss (payoff)" chart3.

The profit or loss at expiry of a forward contract is a straight line proportional to the price difference. The profit or loss of an option is a line that bends at the strike price.

Long call: loss capped at the premium

The loss of a call buyer is limited to the premium paid4. When the price at expiry is above the strike price, the profit or loss is "price at expiry − strike price − premium", and profit grows as the price rises2. The price at expiry at which the profit or loss is zero is called the break-even point. For a long call, it is the strike price plus the premium5. In the example above, it is 100 + 5, or 105 yen. Above 105 yen the buyer makes a profit, and below it the buyer makes a loss.

−100+10+20+30+40100Profit/loss (yen)Price of the underlying at expiry (yen)ProfitLossBreakeven 105
Figure 1Profit and loss at expiry of a long call
Figure description

Profit or loss at expiry of buying one unit of a call with a strike price of 100 yen for a premium of 5 yen. The horizontal axis is the price of the underlying at expiry, and the vertical axis is the profit or loss per unit, including the premium. At 100 yen or less the call is not exercised, and the profit or loss stays at −5 yen. Above 100 yen, each 1 yen rise in the price adds 1 yen to the profit or loss, which reaches zero at 105 yen (the break-even point) and a 15 yen profit at 120 yen. The loss is at most 5 yen, and there is no cap on profit.

Short call: profit capped at the premium

The profit of a call seller is limited to the premium received, and there is no cap on the loss6. In return for the premium, the seller takes on the obligation to sell the underlying at the strike price if the buyer exercises. For the seller of the call in the example, if the price at expiry is 100 yen or less, the call is not exercised and the 5 yen received is kept as profit. Above 100 yen, the call is exercised and the profit or loss is "strike price − price at expiry + premium"2. The break-even point is 105 yen, the same as for the buyer. At a price of 120 yen at expiry the seller loses 15 yen, and at 140 yen the seller loses 35 yen.

−40−30−20−100+10100Profit/loss (yen)Price of the underlying at expiry (yen)ProfitLossBreakeven 105
Figure 2Profit and loss at expiry of a short call
Figure description

Profit or loss at expiry of selling one unit of a call with a strike price of 100 yen for a premium of 5 yen. The horizontal axis is the price of the underlying at expiry, and the vertical axis is the profit or loss per unit, including the premium. At 100 yen or less the call is not exercised, and the profit or loss stays at the 5 yen premium received. Above 100 yen, each 1 yen rise in the price takes 1 yen off the profit or loss, which reaches zero at 105 yen (the break-even point) and a 15 yen loss at 120 yen. The profit is at most 5 yen, and there is no cap on loss.

A long put profits when the price falls

A put buyer makes a profit when the price at expiry is below the strike price minus the premium7. Consider a hypothetical example in which you buy one unit of a put, the right to sell the underlying at a strike price of 100 yen, for a premium of 5 yen. If the price at expiry is below 100 yen, the buyer exercises the right, buys the underlying at the market price, sells it at the strike price of 100 yen, and keeps the difference. The profit or loss is "strike price − price at expiry − premium"8. The break-even point is 100 − 5, or 95 yen, and at a price of 80 yen at expiry the buyer makes a 15 yen profit. At 100 yen or more, the buyer lets the right lapse, and the loss is at most the 5 yen paid. Profit grows as the price falls. Assuming the price of the underlying cannot fall below zero, the largest profit is 95 yen (100 − 5), at a price of zero9.

−100+10+20+30+40100Profit/loss (yen)Price of the underlying at expiry (yen)ProfitLossBreakeven 95
Figure 3Profit and loss at expiry of a long put
Figure description

Profit or loss at expiry of buying one unit of a put with a strike price of 100 yen for a premium of 5 yen. The horizontal axis is the price of the underlying at expiry, and the vertical axis is the profit or loss per unit, including the premium. At 100 yen or more the put is not exercised, and the profit or loss stays at −5 yen. Below 100 yen, each 1 yen fall in the price adds 1 yen to the profit or loss, which reaches zero at 95 yen (the break-even point) and a 15 yen profit at 80 yen. The loss is at most 5 yen, and the profit is largest, at 95 yen, when the price is zero.

A short put loses more as the price falls

The profit of a put seller is limited to the premium received, and the loss grows as the price at expiry falls8. For the seller of the put in the example, if the price at expiry is 100 yen or more, the put is not exercised and the 5 yen received is kept as profit. Below 100 yen, the put is exercised and the seller must buy the underlying at the strike price of 100 yen, so the profit or loss is "price at expiry − strike price + premium"8. The break-even point is 95 yen, the same as for the buyer, and at a price of 80 yen at expiry the seller loses 15 yen. The loss is largest at a price of zero, at 95 yen, which is 19 times the premium received.

−40−30−20−100+10100Profit/loss (yen)Price of the underlying at expiry (yen)ProfitLossBreakeven 95
Figure 4Profit and loss at expiry of a short put
Figure description

Profit or loss at expiry of selling one unit of a put with a strike price of 100 yen for a premium of 5 yen. The horizontal axis is the price of the underlying at expiry, and the vertical axis is the profit or loss per unit, including the premium. At 100 yen or more the put is not exercised, and the profit or loss stays at the 5 yen premium received. Below 100 yen, each 1 yen fall in the price takes 1 yen off the profit or loss, which reaches zero at 95 yen (the break-even point) and a 15 yen loss at 80 yen. The profit is at most 5 yen, and the loss is largest, at 95 yen, when the price is zero.

Comparing the four positions

For the same option, the buyer's and seller's profit or loss differ only in sign at every price at expiry, so they add up to zero10. The table below lists the break-even point and the maximum profit and loss of the four positions in the example with a strike price of 100 yen and a premium of 5 yen. The break-even point is the same for the buyer and the seller5.

Position Break-even point (yen) Maximum profit (yen) Maximum loss (yen)
Long call 105 Unlimited 5
Short call 105 5 Unlimited
Long put 95 95 5
Short put 95 5 95

The buyer's profit is the seller's loss, and the buyer's loss (the premium paid) is the seller's profit10. As a result, the profit and loss chart of a short position is the chart of the long position flipped upside down across the zero line.

The profit or loss of combinations of options with different strike prices, or of options with the underlying asset (spreads, straddles, and others), is covered in Option Strategies.

Premium and the break-even point

The higher the premium, the further the buyer's break-even point is from the strike price, and the larger the buyer's maximum loss and the seller's maximum profit. If the premium of the example call rises from 5 yen to 8 yen, the break-even point of the long call moves from 105 yen to 108 yen, 8 yen away from the strike price, and the maximum loss becomes 8 yen. The premium is higher when the volatility (the size of price moves) of the underlying is higher11.

The simulator below does not take the premium as an input. It calculates the premium from volatility, assuming a current price of the underlying of 100, one year to expiry, and an interest rate of zero. The premium of the initial long call (strike price 100, volatility 20%) is 7.97, not the 5 in the text's example. The break-even point is 107.97, the maximum loss is 7.97, and there is no cap on profit. If you switch to a long put, the premium is the same 7.97, and the break-even point and the maximum profit are both 92.03.

SimulatorProfit and loss at expiry of a single option
Inputs
%
−10010203040708090100110120130Profit/loss per unitUnderlying price at expiry107.97
  • Profit/loss at expiry (incl. premiums)
  • Profit/loss excluding premiums
Long call (strike 100)
Pays premium of 7.97
Breakeven
107.97
Maximum profit
Unlimited
Maximum loss
7.97

Simplifications

  • Premiums are Black-Scholes prices with a current underlying price of 100, 1 year to expiry, a 0% interest rate, and no dividends.
  • With a 0% interest rate, the timing gap between paying the premium and expiry is ignored.
  • Options are European (exercisable only at expiry); only the profit/loss at expiry is shown, not changes in value before expiry.
  • Figures are per unit and ignore fees, taxes, and margin.

This simulator uses simplified calculations for learning. It cannot be used for valuing actual transactions or managing their risk. (Disclaimer)

About this simulator

Under "Product and strategy", switch between the four single-option positions (long call, short call, long put, short put), and move the strike price and volatility to see how the profit and loss line at expiry, the break-even point, and the maximum profit and loss change. The chart also shows the profit and loss line without the premium (the payoff). Raising volatility makes the premium higher and moves the break-even point away from the strike price.

Notes

  1. Osaka Exchange, "決済方法（オプション）" (Settlement methods: options, in Japanese), "SQ値による決済" (Settlement at the SQ value). It gives the profit or loss of a long call as "（SQ値 － 権利行使価格） × 取引単位 × 数量 － 支払いプレミアム" ((SQ value − strike price) × trading unit × quantity − premium paid, our translation). ↩

  2. Central Council for Financial Services Information, "3-4 オプション取引の損益（やさしいデリバティブ）" (Profit and loss from option trading, Easy Derivatives, in Japanese), the section on calls. It shows the formulas for the buyer's and seller's profit or loss with an example of a strike price of 1,000 yen and a premium of 100 yen. ↩ ↩2 ↩3

  3. Japan Exchange Group, "国債先物オプション入門" (Introduction to JGB Futures Options, in Japanese), by Takahiro Hattori, 2022, pages 24–25. It calls Figure 12 "コール・オプションの損益（ペイオフ）の図" (a chart of the profit and loss (payoff) of a call option, our translation). The line at expiry in Figure 12 does not subtract the premium and runs along the horizontal axis at zero profit or loss up to the strike price. ↩

  4. Central Council for Financial Services Information, "3-4 オプション取引の損益（やさしいデリバティブ）" (Profit and loss from option trading, Easy Derivatives, in Japanese), "オプション取引の買い手の立場" (The position of the buyer in option trading). ↩

  5. Kansai University (Koji Ota), "企業財務論2010 Lecture Note 28 オプション取引 Part 1" (Corporate Finance 2010, Lecture Note 28: Option Trading, Part 1, in Japanese), sections 2.1–2.4 (pages 2–4). It gives the break-even point of a call as "権利行使価格＋プレミアム" (strike price + premium, our translation) and of a put as "権利行使価格－プレミアム" (strike price − premium, our translation). ↩ ↩2

  6. Central Council for Financial Services Information, "3-4 オプション取引の損益（やさしいデリバティブ）" (Profit and loss from option trading, Easy Derivatives, in Japanese), "オプション取引の売り手の立場" (The position of the seller in option trading). ↩

  7. Kansai University (Koji Ota), "企業財務論2010 Lecture Note 28 オプション取引 Part 1" (Corporate Finance 2010, Lecture Note 28: Option Trading, Part 1, in Japanese), section 2.3, "プットの買い" (Buying a put), page 3. ↩

  8. Central Council for Financial Services Information, "3-4 オプション取引の損益（やさしいデリバティブ）" (Profit and loss from option trading, Easy Derivatives, in Japanese), the section on puts. ↩ ↩2 ↩3

  9. The Central Council for Financial Services Information describes the loss of a seller as having no upper limit, and Kansai University as unlimited. The Options Industry Council, "Long Straddle", under "Max Gain", limits the profit because "the stock price cannot go below zero", and the text follows this. ↩

  10. Central Council for Financial Services Information, "3-4 オプション取引の損益（やさしいデリバティブ）" (Profit and loss from option trading, Easy Derivatives, in Japanese), the tables of profit and loss for calls and for puts. In the example with a strike price of 1,000 yen and a premium of 100 yen, the final profit or loss of the buyer and the seller differ only in sign at every price. ↩ ↩2

  11. Kansai University (Koji Ota), "企業財務論2010 Lecture Note 28 オプション取引 Part 1" (Corporate Finance 2010, Lecture Note 28: Option Trading, Part 1, in Japanese), section 4, "オプション・プレミアムの決定要因" (Factors that determine the option premium), page 7. ↩