Black-Scholes option price

Price a European option (call or put) with the Black-Scholes-Merton model, plus the greeks (delta, gamma, vega, theta, rho). Send POST /api/black-scholes with the required fields type, spot, strike, timeToExpiryYears and 2 more and pay $0.002 per call over x402 or MPP, or call it free by solving a proof-of-work challenge. It returns a JSON object with type, price, delta, gamma, vega and 4 more.

Continuous dividend yield supported. Greeks are per unit: theta is per year, vega per 1.00 change in volatility, rho per 1.00 change in rate. Deterministic - matches standard references to the cent.

Category: Live public data · Tags: finance options black-scholes derivatives greeks call put

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Parameters

Example request

curl -i -X POST https://agent402.tools/api/black-scholes \
  -H "Content-Type: application/json" \
  -d '{"type":"call","spot":100,"strike":100,"timeToExpiryYears":1,"riskFreeRate":0.05,"volatility":0.2,"dividendYield":0}'

Without payment this returns HTTP 402 Payment Required with the exact price for black-scholes; any x402 v2 or MPP client pays it and retries.

Example response

{
  "type": "call",
  "price": 10.4506,
  "delta": 0.6368,
  "gamma": 0.0188,
  "vega": 37.524,
  "theta": -6.414,
  "rho": 53.2325,
  "d1": 0.35,
  "d2": 0.15
}

From an MCP client

catalog.call {
  "slug": "black-scholes",
  "params": {
    "type": "call",
    "spot": 100,
    "strike": 100,
    "timeToExpiryYears": 1,
    "riskFreeRate": 0.05,
    "volatility": 0.2,
    "dividendYield": 0
  }
}

On the hosted connector at https://agent402.tools/mcp, catalog.call runs black-scholes free (rate-limited, no wallet). Local install: npx -y agent402-mcp.

Errors and behavior

• type, spot, strike, timeToExpiryYears, riskFreeRate and volatility are required. An input the tool rejects returns an HTTP 4xx whose body carries error, tool, expected, required and example, so the caller can correct it.
• A paid call that ends in any status of 400 or above is not charged over x402, MPP or a prepaid credits key: settlement is cancelled when the tool fails. The exception is a Tempo push credential, a transfer the buyer sent before the call: it settles before the tool runs, so if the tool then fails the payment is recorded as a refund owed to the paying wallet.
• Free tier: no outbound network call leaves the server for this tool, so proof-of-work (16 leading zero bits of sha256) pays for it.
• A GET or HEAD to /api/black-scholes returns the same 402 quote, so the price can be read without a body.
• An Idempotency-Key header makes a retried paid call replay the first 200 instead of charging again (an answer larger than 1 MB is not replayed).

Paid call (JavaScript agent)

import { wrapFetchWithPayment } from "@x402/fetch";
import { x402Client } from "@x402/core/client";
import { registerExactEvmScheme } from "@x402/evm/exact/client";
import { privateKeyToAccount } from "viem/accounts";

const client = new x402Client();
client.setSpendControls?.(false); // keep your own spending ceiling in code
registerExactEvmScheme(client, { signer: privateKeyToAccount(KEY) });
const payFetch = wrapFetchWithPayment(fetch, client);

const res = await payFetch("https://agent402.tools/api/black-scholes", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({
    "type": "call",
    "spot": 100,
    "strike": 100,
    "timeToExpiryYears": 1,
    "riskFreeRate": 0.05,
    "volatility": 0.2,
    "dividendYield": 0
  }),
});

No wallet? Pay with compute

Fetch a challenge, solve the sha256 puzzle (16 leading zero bits, a fraction of a second of CPU), and resend with the X-Pow-Solution header:

import { createHash } from "node:crypto";
const lz = (b) => { let t = 0; for (const x of b) { if (!x) { t += 8; continue; } t += Math.clz32(x) - 24; break; } return t; };
const c = await (await fetch("https://agent402.tools/api/pow/challenge?slug=black-scholes")).json();
let n = 0;
while (lz(createHash("sha256").update(c.challenge + ":" + n).digest()) < c.difficulty) n++;
await fetch("https://agent402.tools/api/black-scholes", { method: "POST", headers: { "X-Pow-Solution": c.token + ":" + n, "Content-Type": "application/json" }, body: JSON.stringify({"type":"call","spot":100,"strike":100,"timeToExpiryYears":1,"riskFreeRate":0.05,"volatility":0.2,"dividendYield":0}) });

Part of these workflows

Black-Scholes option price is one step in this skill pack, each sold as a single call:

• Options analytics - Price a European option on a live stock: pull the current quote, estimate volatility from recent history, run Black-Scholes for fair value + the full greeks, and check the news for catalysts.

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