Option pricing & greeks (Black-Scholes) API

Price a European call or put with the Black-Scholes model and return all greeks (delta, gamma, vega, theta, rho). Answers queries like 'price this option', 'what is the delta of this call', 'black scholes value', 'option greeks'.

Price$0.03per request

MethodPOST

Route/v1/finance/black-scholes

StatusLive

MIME typeapplication/json

Rate limit120/minute

CacheNo cache

financeoptionsblack-scholesgreeksdeltaderivativespricingvolatility

API URLhttps://x402.hexl.dev/v1/finance/black-scholes

Integration docs

Example request

{
  "spot": 100,
  "strike": 105,
  "timeToExpiry": 0.5,
  "rate": 0.05,
  "volatility": 0.2,
  "type": "call"
}

Example response

{
  "price": 4.04,
  "greeks": {
    "delta": 0.45,
    "gamma": 0.027,
    "vega": 0.27,
    "theta": -0.017,
    "rho": 0.2
  },
  "inputs": {
    "spot": 100,
    "strike": 105,
    "timeToExpiry": 0.5,
    "rate": 0.05,
    "volatility": 0.2,
    "type": "call",
    "dividendYield": 0
  }
}

Input schema

{
  "type": "object",
  "required": [
    "spot",
    "strike",
    "timeToExpiry",
    "rate",
    "volatility",
    "type"
  ],
  "properties": {
    "spot": {
      "type": "number",
      "examples": [
        100
      ]
    },
    "strike": {
      "type": "number",
      "examples": [
        105
      ]
    },
    "timeToExpiry": {
      "type": "number",
      "description": "years",
      "examples": [
        0.5
      ]
    },
    "rate": {
      "type": "number",
      "description": "risk-free, decimal",
      "examples": [
        0.05
      ]
    },
    "volatility": {
      "type": "number",
      "description": "annualized, decimal",
      "examples": [
        0.2
      ]
    },
    "type": {
      "type": "string",
      "enum": [
        "call",
        "put"
      ]
    },
    "dividendYield": {
      "type": "number",
      "default": 0
    }
  }
}

Output schema

{
  "type": "object",
  "required": [
    "price",
    "greeks"
  ],
  "properties": {
    "price": {
      "type": "number"
    },
    "greeks": {
      "type": "object",
      "properties": {
        "delta": {
          "type": "number"
        },
        "gamma": {
          "type": "number"
        },
        "vega": {
          "type": "number"
        },
        "theta": {
          "type": "number"
        },
        "rho": {
          "type": "number"
        }
      }
    },
    "inputs": {
      "type": "object",
      "additionalProperties": true
    }
  }
}