# What is my options profit?

Computes the profit or loss of buying or selling a call or put option at expiration, its break-even price, most profit and most loss, and its Black-Scholes value before expiration, with payoff charts.

- Page: https://www.acalculator.org/finance/options-profit-calculator
- JSON spec: https://www.acalculator.org/finance/options-profit-calculator.json
- Version: 7e9fc12bc07b

## Default answer

Example with the default inputs (Option Call, You Buy, Strike price $100.00, Premium per share $5.00, Contracts 1, Stock price at expiration $115.00, Stock price now $100.00, Volatility (yearly) 30%, Risk-free rate (yearly) 4%, Days to expiration 30, Dividend yield (yearly) 0%): If the stock is at $115.00 at expiration, this option position gives $1,000.00.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| type | Option | A call (the right to buy at the strike) or a put (the right to sell at the strike). |
| side | You | Whether you buy the option (pay the premium) or sell (write) it (receive the premium). |
| strike | Strike price | The price per share at which the option lets its owner buy (call) or sell (put) the stock. |
| premium | Premium per share | The option price per share, as quoted. One contract costs 100 times this. |
| contracts | Contracts | How many contracts. Each standard contract covers 100 shares. |
| at | Stock price at expiration | The stock price on the expiration date you want to check. |
| spot | Stock price now | Today’s stock price, typed. Leave empty to skip the value before expiration. |
| vol | Volatility (yearly) | The expected yearly volatility of the stock, in percent (for example the implied volatility). |
| rate | Risk-free rate (yearly) | A yearly risk-free interest rate, such as a Treasury bill yield, in percent. Empty counts as 0%. |
| days | Days to expiration | Calendar days until the option expires. |
| div | Dividend yield (yearly) | The stock’s yearly dividend yield, in percent. Empty counts as 0%. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| profit | Profit or loss at expiration | The option’s value at expiration minus the premium, times the shares; the other way round when you sell. |
| returnPct | Return on premium | The profit or loss as a percent of the total premium paid or received. |
| breakEven | Break-even stock price | The stock price at expiration with no profit or loss: strike + premium for a call, strike − premium for a put. |
| maxProfit | Most you can make | The largest profit at expiration, or Unlimited. |
| maxLoss | Most you can lose | The largest loss at expiration, as a positive amount, or Unlimited. |
| premiumTotal | Total premium | Premium per share × 100 × contracts: paid when you buy, received when you sell. |
| value | Black-Scholes value now | The model value of one option on one share today, from the stock price now, volatility, rate and days. |
| profitNow | Profit or loss if closed now | The Black-Scholes value minus the premium, times the shares; the other way round when you sell. |
| delta | Delta | How much the option value moves for a $1 move in the stock, per share, for the buyer. |

## Method

At expiration a call is worth max(S − K, 0) and a put max(K − S, 0) per share; profit = (value − premium) × 100 × contracts for a buyer, the negative for a seller. Before expiration: Black-Scholes-Merton, C = S e^(−qT) N(d₁) − K e^(−rT) N(d₂), P = K e^(−rT) N(−d₂) − S e^(−qT) N(−d₁).

## Assumptions

- Every price, the volatility and the rate are typed; no quote is looked up.
- Each contract covers 100 shares. Commissions and taxes are not included.
- The Black-Scholes value is for a European option held to its expiry, with a constant volatility, rate and dividend yield (continuously compounded) and T = days ÷ 365. An American option can be worth a little more.
- This is an estimate, not investment advice.

## Worked examples

1. type = call, side = buy, strike = $70.00, premium = $2.20, contracts = 1, at = $65.00 gives profit = -$220.00, premiumTotal = $220.00, breakEven = $72.20, maxLoss = $220.00, maxProfit = Unlimited, returnPct = -100%. Source: SEC Investor.gov, An Introduction to Options, Investor Bulletin: break even at $72.20 and a $220 loss when the call expires worthless (https://www.investor.gov/introduction-investing/general-resources/news-alerts/alerts-bulletins/investor-bulletins-63).
2. type = put, side = buy, strike = $70.00, premium = $2.20, contracts = 1, at = $60.00 gives profit = $780.00, breakEven = $67.80, maxProfit = $6,780.00, maxLoss = $220.00. Source: SEC Investor.gov, An Introduction to Options, Investor Bulletin: the ABC December 70 put at $2.20 breaks even at $67.80 (https://www.investor.gov/introduction-investing/general-resources/news-alerts/alerts-bulletins/investor-bulletins-63).
3. type = call, side = buy, strike = $40.00, premium = $3.00, contracts = 1, at = $42.00, spot = $42.00, vol = 20%, rate = 10%, days = 182.5, div = 0% gives value = $4.76, profit = -$100.00, profitNow = $175.94, delta = 0.779131. Source: Hull (2018), Options, Futures, and Other Derivatives, 10th edition, chapter 15: the call is worth $4.76.
4. type = put, side = buy, strike = $40.00, premium = $1.00, contracts = 1, at = $42.00, spot = $42.00, vol = 20%, rate = 10%, days = 182.5, div = 0% gives value = $0.81, profit = -$100.00, delta = -0.220869. Source: Hull (2018), Options, Futures, and Other Derivatives, 10th edition, chapter 15: the put is worth $0.81.
5. type = call, side = sell, strike = $100.00, premium = $5.00, contracts = 2, at = $120.00 gives profit = -$3,000.00, maxProfit = $1,000.00, maxLoss = Unlimited, breakEven = $105.00, returnPct = -300%. Source: SEC Investor.gov, An Introduction to Options, Investor Bulletin: the writer of a call must sell at the strike (https://www.investor.gov/introduction-investing/general-resources/news-alerts/alerts-bulletins/investor-bulletins-63).

## FAQ

### How do I calculate the profit on a call option?

At expiration a call is worth the stock price minus the strike, or nothing if the stock is below the strike. Take off the premium and multiply by 100 shares per contract. A call with a $70 strike bought for $2.20 is worth $10 a share with the stock at $80: (10 − 2.20) × 100 = $780 profit. If the stock ends at $65 the call expires worthless and you lose the $220 premium.

### How do I calculate the profit on a put option?

At expiration a put is worth the strike minus the stock price, or nothing if the stock is above the strike. A put with a $70 strike bought for $2.20 is worth $10 a share with the stock at $60: (10 − 2.20) × 100 = $780 profit.

### What is the break-even price of an option?

For a call it is the strike plus the premium; for a put, the strike minus the premium. The SEC’s example: a $70 call bought for $2.20 breaks even at $72.20, and a $70 put at $2.20 breaks even at $67.80. It is the same price for the buyer and the seller.

### What happens when I sell (write) an option?

You receive the premium, and your profit and loss are the buyer’s turned around. The most you can make is the premium. Writing a call can lose without limit, because the stock can keep rising; writing a put can lose up to the strike minus the premium, times 100 shares.

### What does the Black-Scholes value mean?

It is a model price for the option today, before expiration, from the stock price now, the strike, the volatility, the risk-free rate, the days left and the dividend yield. Hull’s textbook example (stock $42, strike $40, 20% volatility, 10% rate, six months) gives a call worth $4.76 and a put worth $0.81. The “if closed now” profit compares that value with your premium.

### Why does the value before expiration differ from the value at expiration?

Before expiration an option also has time value: the chance that the stock moves further before the option expires. That is why the “if closed now” line is a curve that lies above the expiration payoff for a buyer. On the expiration date the time value is gone.

### Does the calculator fetch option quotes?

No. You type the premium, the stock prices, the volatility and the rate, so the page never sends anything and gives the same answer every time. Take them from your broker’s option chain.

## Sources

- U.S. Securities and Exchange Commission, Investor.gov: An Introduction to Options, Investor Bulletin. https://www.investor.gov/introduction-investing/general-resources/news-alerts/alerts-bulletins/investor-bulletins-63
- J. C. Hull (2018), Options, Futures, and Other Derivatives, 10th edition, chapters 10 and 15: option payoffs and the Black-Scholes-Merton model.
- F. Black and M. Scholes (1973), The Pricing of Options and Corporate Liabilities, Journal of Political Economy 81(3): 637–654. https://doi.org/10.1086/260062
- R. C. Merton (1973), Theory of Rational Option Pricing, Bell Journal of Economics and Management Science 4(1): 141–183 (a continuous dividend yield). https://doi.org/10.2307/3003143