{
  "x402Version": 2,
  "id": 33409,
  "slug": "33409",
  "resource": "https://api.edifiedlab.com/v1/market/black-scholes",
  "description": "Black-Scholes option price and Greeks (delta, gamma, vega, theta) from JSON keys spot, strike, tau (years; 3-month = 0.25), sigma (annualized volatility), and is_call (boolean). Pure closed-form calculation, no market data looked up or stored. vega is ∂price/∂sigma per 1.0 volatility (not per 1%).",
  "type": "http",
  "resourceType": "Security",
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      "amount": "11000",
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      "maxTimeoutSeconds": 600
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      "example": {
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          "action": {
            "const": "calculate",
            "type": "string"
          },
          "delta": {
            "type": "number"
          },
          "gamma": {
            "type": "number"
          },
          "payload": {
            "const": "black_scholes",
            "type": "string"
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          "price": {
            "type": "number"
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          "theta_per_day": {
            "type": "number"
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          "vega": {
            "description": "∂price/∂sigma per 1.0 vol",
            "type": "number"
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            "sigma": 0.2,
            "spot": 100,
            "strike": 100,
            "tau": 0.25
          },
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          "method": "POST",
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            "delta": 0.5199388058,
            "gamma": 0.0398443914,
            "payload": "black_scholes",
            "price": 3.9877611677,
            "theta_per_day": -0.0218325432,
            "vega": 19.9221957047
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                    "type": "boolean"
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                  "rate": {
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                    "description": "annualized risk-free rate (optional; default 0)",
                    "type": "number"
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                  "sigma": {
                    "description": "annualized volatility",
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                  "strike": {
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                    "type": "number"
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                    "type": "number"
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                  "delta": {
                    "type": "number"
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                  "gamma": {
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                  "price": {
                    "type": "number"
                  },
                  "theta_per_day": {
                    "type": "number"
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                    "description": "∂price/∂sigma per 1.0 vol",
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  "sourceHost": "api.edifiedlab.com",
  "lastUpdated": "2026-09-16T12:58:39.46Z",
  "quality": {
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    "uniquePayers30d": 1,
    "lastCalledAt": "2026-09-16T12:58:39.149Z"
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  "metadata": {
    "extensions": {
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              "is_call": true,
              "sigma": 0.2,
              "spot": 100,
              "strike": 100,
              "tau": 0.25
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            "example": {
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              "gamma": 0.0398443914,
              "payload": "black_scholes",
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                    "spot": {
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                    "strike": {
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                    "tau": {
                      "description": "time to expiry in years (3-month = 0.25)",
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                    "gamma": {
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                      "type": "string"
                    },
                    "price": {
                      "type": "number"
                    },
                    "theta_per_day": {
                      "type": "number"
                    },
                    "vega": {
                      "description": "∂price/∂sigma per 1.0 vol",
                      "type": "number"
                    }
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  "featured": false,
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    "submitted_at": "2026-10-14T01:15:01.050Z"
  },
  "exampleResponse": {
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    "gamma": 0.0398443914,
    "payload": "black_scholes",
    "price": 3.9877611677,
    "theta_per_day": -0.0218325432,
    "vega": 19.9221957047
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}