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). 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.

Input

Field	Type	Description
type *	string	"call" or "put"
spot *	number	Current underlying price (S)
strike *	number	Strike price (K)
timeToExpiryYears *	number	Time to expiry in years (T)
riskFreeRate *	number	Annual risk-free rate as decimal (r)
volatility *	number	Annual volatility as decimal (sigma)
dividendYield	number	Continuous dividend yield as decimal (q). Default 0.

Example output

{
  "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
}

Try it — see the 402 challenge (free)

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}'

The response is HTTP 402 Payment Required with exact payment requirements. Any x402 v2 client pays automatically and retries:

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();
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

This is a pure-CPU tool, so an agent without a wallet can pay with proof-of-work instead of USDC: fetch a challenge, solve the sha256 puzzle (16 leading zero bits — a fraction of a second of CPU, no money, no AI tokens), 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

This tool is one step in a curated multi-tool workflow — agents can fetch the whole sequence as an MCP prompt or call https://agent402.tools/api/skill-packs/{slug}/prompt.

• 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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