{
  "id": "options-profit",
  "version": "7e9fc12bc07b",
  "status": "published",
  "name": "Options Profit Calculator",
  "question": "What is my options profit?",
  "summary": "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.",
  "category": "finance",
  "subcategory": "investing",
  "url": "https://www.acalculator.org/finance/options-profit-calculator",
  "markdown": "https://www.acalculator.org/finance/options-profit-calculator.md",
  "kind": "function",
  "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."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "type": {
        "title": "Option",
        "description": "A call (the right to buy at the strike) or a put (the right to sell at the strike).",
        "type": "string",
        "enum": [
          "call",
          "put"
        ]
      },
      "side": {
        "title": "You",
        "description": "Whether you buy the option (pay the premium) or sell (write) it (receive the premium).",
        "type": "string",
        "enum": [
          "buy",
          "sell"
        ]
      },
      "strike": {
        "title": "Strike price",
        "description": "The price per share at which the option lets its owner buy (call) or sell (put) the stock.",
        "type": "number",
        "x-unit": "USD",
        "exclusiveMinimum": 0,
        "maximum": 1000000
      },
      "premium": {
        "title": "Premium per share",
        "description": "The option price per share, as quoted. One contract costs 100 times this.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0,
        "maximum": 1000000
      },
      "contracts": {
        "title": "Contracts",
        "description": "How many contracts. Each standard contract covers 100 shares.",
        "type": "integer",
        "minimum": 1,
        "maximum": 100000
      },
      "at": {
        "title": "Stock price at expiration",
        "description": "The stock price on the expiration date you want to check.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0,
        "maximum": 10000000
      },
      "spot": {
        "title": "Stock price now",
        "description": "Today’s stock price, typed. Leave empty to skip the value before expiration.",
        "type": "number",
        "x-unit": "USD",
        "exclusiveMinimum": 0,
        "maximum": 10000000
      },
      "vol": {
        "title": "Volatility (yearly)",
        "description": "The expected yearly volatility of the stock, in percent (for example the implied volatility).",
        "type": "number",
        "x-unit": "percent",
        "exclusiveMinimum": 0,
        "maximum": 500
      },
      "rate": {
        "title": "Risk-free rate (yearly)",
        "description": "A yearly risk-free interest rate, such as a Treasury bill yield, in percent. Empty counts as 0%.",
        "type": "number",
        "x-unit": "percent",
        "minimum": -10,
        "maximum": 50
      },
      "days": {
        "title": "Days to expiration",
        "description": "Calendar days until the option expires.",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 3650
      },
      "div": {
        "title": "Dividend yield (yearly)",
        "description": "The stock’s yearly dividend yield, in percent. Empty counts as 0%.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 50
      }
    }
  },
  "outputs": {
    "profit": {
      "label": "Profit or loss at expiration",
      "description": "The option’s value at expiration minus the premium, times the shares; the other way round when you sell.",
      "format": "money"
    },
    "returnPct": {
      "label": "Return on premium",
      "description": "The profit or loss as a percent of the total premium paid or received.",
      "format": "percent"
    },
    "breakEven": {
      "label": "Break-even stock price",
      "description": "The stock price at expiration with no profit or loss: strike + premium for a call, strike − premium for a put.",
      "format": "money"
    },
    "maxProfit": {
      "label": "Most you can make",
      "description": "The largest profit at expiration, or Unlimited.",
      "format": "money"
    },
    "maxLoss": {
      "label": "Most you can lose",
      "description": "The largest loss at expiration, as a positive amount, or Unlimited.",
      "format": "money"
    },
    "premiumTotal": {
      "label": "Total premium",
      "description": "Premium per share × 100 × contracts: paid when you buy, received when you sell.",
      "format": "money"
    },
    "value": {
      "label": "Black-Scholes value now",
      "description": "The model value of one option on one share today, from the stock price now, volatility, rate and days.",
      "format": "money"
    },
    "profitNow": {
      "label": "Profit or loss if closed now",
      "description": "The Black-Scholes value minus the premium, times the shares; the other way round when you sell.",
      "format": "money"
    },
    "delta": {
      "label": "Delta",
      "description": "How much the option value moves for a $1 move in the stock, per share, for the buyer.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "type": "call",
      "side": "buy",
      "strike": 100,
      "premium": 5,
      "contracts": 1,
      "at": 115,
      "spot": 100,
      "vol": 30,
      "rate": 4,
      "days": 30,
      "div": 0
    },
    "outputs": {
      "profit": 1000,
      "returnPct": 200,
      "breakEven": 105,
      "maxProfit": "Unlimited",
      "maxLoss": 500,
      "premiumTotal": 500,
      "value": 3.5911230320233614,
      "profitNow": -140.88769679766386,
      "delta": 0.5323701379534023
    },
    "text": "If the stock is at $115.00 at expiration, this option position gives $1,000.00."
  },
  "examples": [
    {
      "given": {
        "type": "call",
        "side": "buy",
        "strike": 70,
        "premium": 2.2,
        "contracts": 1,
        "at": 65
      },
      "expect": {
        "profit": -220,
        "premiumTotal": 220,
        "breakEven": 72.2,
        "maxLoss": 220,
        "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)"
    },
    {
      "given": {
        "type": "put",
        "side": "buy",
        "strike": 70,
        "premium": 2.2,
        "contracts": 1,
        "at": 60
      },
      "expect": {
        "profit": 780,
        "breakEven": 67.8,
        "maxProfit": 6780,
        "maxLoss": 220
      },
      "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); hand calculation in content.mdx"
    },
    {
      "given": {
        "type": "call",
        "side": "buy",
        "strike": 40,
        "premium": 3,
        "contracts": 1,
        "at": 42,
        "spot": 42,
        "vol": 20,
        "rate": 10,
        "days": 182.5,
        "div": 0
      },
      "expect": {
        "value": 4.759422392871535,
        "profit": -100,
        "profitNow": 175.9422392871535,
        "delta": 0.779131290942669
      },
      "source": "Hull (2018), Options, Futures, and Other Derivatives, 10th edition, chapter 15: the call is worth $4.76; Python 3 cross-check"
    },
    {
      "given": {
        "type": "put",
        "side": "buy",
        "strike": 40,
        "premium": 1,
        "contracts": 1,
        "at": 42,
        "spot": 42,
        "vol": 20,
        "rate": 10,
        "days": 182.5,
        "div": 0
      },
      "expect": {
        "value": 0.8085993729000958,
        "profit": -100,
        "delta": -0.22086870905733105
      },
      "source": "Hull (2018), Options, Futures, and Other Derivatives, 10th edition, chapter 15: the put is worth $0.81; Python 3 cross-check"
    },
    {
      "given": {
        "type": "call",
        "side": "sell",
        "strike": 100,
        "premium": 5,
        "contracts": 2,
        "at": 120
      },
      "expect": {
        "profit": -3000,
        "maxProfit": 1000,
        "maxLoss": "Unlimited",
        "breakEven": 105,
        "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); hand calculation in content.mdx"
    }
  ],
  "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"
  ],
  "related": [
    "stock",
    "stock-profit",
    "roi",
    "crypto-profit",
    "dividend"
  ],
  "changelog": []
}