{
  "format": "delx/intent-card/v1",
  "id": "bs-delta-api",
  "intent": "Black-Scholes Delta for an agent workflow",
  "title": "Black-Scholes Delta API for agents",
  "description": "Call/put delta from BS closed form. Call when delta-hedging or option inventory needs BS delta. Returns delta for call and put as deterministic JSON for $0.001 USDC via x402 on Base. First-party local math only—no RPC, live market feed, API keys, storage, or mediagen. Advisory only; the caller owns capital, risk, and production controls.",
  "keywords": [
    "Black-Scholes Delta API",
    "Black-Scholes Delta for agents",
    "pay per result API",
    "x402 API",
    "no API key"
  ],
  "updated_at": "2026-08-23",
  "canonical_url": "https://commerce.delx.ai/intents/bs-delta-api",
  "machine_url": "https://commerce.delx.ai/intents/bs-delta-api.json",
  "recommendation": {
    "tool_name": "util_bs_delta",
    "service_name": "Black-Scholes Delta",
    "method": "POST",
    "resource": "https://api.delx.ai/api/v1/x402/bs-delta",
    "price_usdc": "0.001",
    "payment_protocols": [
      "x402",
      "mpp"
    ],
    "input_schema": {
      "type": "object",
      "properties": {
        "spot": {
          "type": "number",
          "description": "Underlying spot price (>0)"
        },
        "strike": {
          "type": "number",
          "description": "Option strike price (>0)"
        },
        "vol": {
          "type": "number",
          "description": "Annualized volatility as decimal (>0), e.g. 0.2 = 20%"
        },
        "t_years": {
          "type": "number",
          "description": "Time to expiry in years (>0)"
        },
        "rate": {
          "type": "number",
          "description": "Risk-free rate as decimal (optional, default 0)"
        }
      },
      "required": [
        "spot",
        "strike",
        "vol",
        "t_years"
      ],
      "additionalProperties": true
    },
    "example_input": {
      "spot": 100,
      "strike": 100,
      "vol": 0.2,
      "t_years": 0.25,
      "rate": 0
    },
    "example_output": {
      "schema": "delx/util-bs-delta/v1",
      "delta_call": 0.5199388058383725,
      "delta_put": -0.4800611941616275
    },
    "agentcash": {
      "buy": "npx agentcash@latest fetch https://api.delx.ai/api/v1/x402/bs-delta -m POST -H 'x-delx-source: intent-card-bs-delta-api' --max-amount 0.001 -b '{\"spot\":100,\"strike\":100,\"vol\":0.2,\"t_years\":0.25,\"rate\":0}'",
      "max_amount_usdc": "0.001"
    }
  },
  "attribution": {
    "header": "x-delx-source",
    "value": "intent-card-bs-delta-api"
  },
  "evidence": {
    "paid_openapi": "https://api.delx.ai/openapi.x402.json",
    "governed_portfolio": "https://api.delx.ai/x402-portfolio.json",
    "live_contract": "https://api.delx.ai/api/v1/x402/bs-delta"
  }
}